I would say wax candles! Of course, current practice and perception is that oil, and specifically olive oil, is better. But from an halachic perspective, I would say the opposite (at least for floating cork wicks -- but standing wicks may well be a different story).
Firstly, is there any halachic imperative to prefer olive oil over any other oil? The source for this is Shabbat 23a:
As Soncino translates:
R. Joshua b. Levi said: All oils are fit for the Hanukkah lamp, but olive oil is of the best. Abaye observed: At first the Master [Rabbah] used to seek poppy-seed oil, saying, The light of this is more lasting; but when he heard this [dictum] of R. Joshua b. Levi, he was particular for olive oil, saying, This yields a clearer light.Very important to note -- although Soncino translates, "All oils are fit for the Hanukkah lamp," the gemara itself does not specify Chanukka. It is indeed a logical deduction that this refers to the Chanukka lamp, and Tosafot indeed makes this deduction, on the side of the gemara, but one might otherwise interpret this as referring, e.g., to the Shabbat lamp.
R. Joshua b. Levi also said: All oils are fit for ink, and olive oil is of the best. The scholars propounded: for kneading or for smoking? — Come and hear: For R. Samuel b. Zutra recited: All oils are fit for ink, and olive oil is of the best, both for kneading and for smoking. R. Samuel b. Zutra recited it thus: All soots are fit for ink: and olive oil is the best. R. Huna said: All gums are good for ink, but balsam gum is the best of all.
There are a few things we might derive from this gemara. The first important thing to note is that Rabba initially used non-olive oil, for practical purposes. There was no emotional connection to one specific type of oil, but rather it was a cold calculation of which was the best kind of oil for this purpose. And poppy-seed oil seemed to be best, because it burned for longer.
Furthermore, once he heard this dictum of Rabbi Yehoshua ben Levi, he instead went after olive oil preferentially, giving a different reason -- that it burns brighter. One needs to question whether this is really his reason for preferring it. Is brighter better? Or is longer better?
One might well make a homiletical point out of this, and one might even connect it to the nes of the pach shemen. Yet leaving that aside, it certainly seems plausible that Rabba knew well before this that different oils have different properties, and while one may be good in one respect, another might be better in a different respect. Yet he reverses his initial practice when hearing this statement by Rabbi Yehoshua ben Levi. This might be because he wishes to conduct himself in accordance with this tradition from Rabbi Yehoshua ben Levi, and thus now states a factor that would weigh in favor of olive oil. Or alternatively, now that he heard this statement in the name of Rabbi Yehoshua ben Levi, he deduces what aspect of kindling the lights should be prioritized, and apparently that is brightness rather than duration.
Now compare wax candles to olive oil. Which burns longer? Which burns brighter?
This past Chanukka (and previous years as well), we lit olive oil in floating wicks next to wax candles. My father always has lit oil. Yet we kids most often lit candles, initially because these were the projects we came home from school with. This year, I lit olive oil, and Meir came from nursery school with a candle menorah he had made (or more specifically, glued black and white buttons on in order to decorate). So I have had opportunity to compare them side by side.
It seems to me that the flames on wax candles are slightly whiter, while olive oil is a bit more tinged yellow. But this is hardly noticeable. However, this is only true at the very beginning of lighting. As time progresses, the wax candles are much, much brighter than the oil with floating wicks.
Why is this? Well, the size of the flame is based in large part on the amount of oxygen that gets to it. At the start, wax candles and oil cups are equivalent, since the oil is at the top of the cup and so it gets about the same amount of oxygen. (Although, of course, even then, the candles get oxygen from below as well as from above, while the oil only gets from above.) However, as the oil is consumed, the floating wick drops lower and lower in the cup, and less and less oxygen gets to the flame. At this point, the wax candles are much brighter than the oil cups. Indeed, sometimes the flames go out before all the oil is consumed. This may be because the floating wick capsized, but also because not enough oxygen gets to the flame when the floating wick is so low in the cup.
On the other hand, olive oil lasts much, much longer. But which is preferable? I believe the gemara addressed this issue. Rabba initially favored poppy-seed oil, thinking that because it burns longer, it is preferable, but reversed himself when he heard Rabbi Yehoshua ben Levi's statement, and now held that olive oil was preferable because it burns brighter. We may walk away from this gemara with the conclusion that brightness is better than duration. And so, wax candles are better than oil, when the oil is being used with floating wicks.
There is another reason, brought down by Mishnah Brurah, that olive oil was used in the nes of the pach shemen, and is thus preferable. However, this is an additional reason, supplementing the reason given in the gemara. Rabba did not give this reason, and did not even consider this reason initially, when he preferred poppy-seed oil. Should we give precedence to that which is defined as min hamuvchar by the gemara, or to something put forth by Rishonim and Acharonim, who are post-Talmudic, and what was a supplemental reason to boot? I would say that we should give precedence to the gemara.
{Update: To clarify, there are many who said that olive oil is preferable for this reason -- though they would seem to be operating on the assumption that olive oil burned just as brightly as a candle. Some examples: Meiri, Mahari Brona, Mishna Berura, Aruch haShulchan who say this, that olive oil is preferable over wax for this reason, and Kolbo and Levush that this is a reason that olive oil is Min haMuvchar. Others think wax is invalid for other reasons, but many people use wax and do not hold like this opinion.
To cite Encyclopedia Talmudit:
מהדר - לנר חנוכה - אחר שמן שומשום שאורו רב יותר - או שאינו ממהר לכלות כשמן זית - כיון ששמע דברי ר' יהושע בן לוי התחיל להדר אחר שמן זית שאורו צלול יותר. ופסקו ראשונים שמצוה מן המובחר בשמן זית, וכשאינו מצוי, מצוה בשמנים שאורם זך וצלול, וצריך לחזר אחרי שמנים אלו. נרות של שעוה, יש שכתבו שהם מצוה מן המובחר כמו שמן זית, כיון שאורם צלול, ויש ראשונים שכתבו שאף על פי שנרות של שעוה מותרים, נוי מצוה להדליק בשמן, מאחר שהנס היה בשמן. יש מהראשונים שכתבו בטעם שמצוה מן המובחר בשמן זית, לפי שבו היה הנס, ולפיכך מצוה בשמן זית יותר מבנרות שעוה. וכתבו אחרונים שאין צריך לחזר אחר שמן זית, ויש שכתבו שמצוה להדר אחר שמן זית אפילו אם הוא ביוקר. ויש שכתבו שמצוה מן המובחר בשמן זית, ואם אינו מצוי, מצוה בשאר שמנים, ואם אינם מצויים, נרות שעוה מהודרים יותר משומן או חלב.
ויש מן האחרונים שחולק וסובר שנר של שעוה או של חלב הכרוכים על הפתילה פסולים לחנוכה, לפי שהנס נעשה בנר, ואינו קרוי נר - בלשון התלמוד - אלא כשיש בו שמן, שאין האור שולט בכל השמן אלא בראש הפתילה ומושך משם את השמן אליו, אבל של שעוה או של חלב אינו קרוי נר אלא אבוקה, שכיון שהאור הולך אחר הפתילה, נמצא שהאור והלהבה שולטים בכל השעוה, ואבוקה פסולה לנר חנוכה
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Perhaps since the gemara (namely, Rabba) maintains that olive oil is min hamuvchar because it is brighter, we should say that olive oil, throughout its burning, is bright enough to be considered min hamuvchar, and more than that does not add anything? While possible, I would not say this, in part because poppy-seed oil is also (presumably) bright enough, but since there is something brighter, it is better to go after that type of oil. That is, we seek after more brightness -- quite possibly because this increases pirsumei nissa -- and choose the one brightest from all that is available to us. Keeping with this goal, we should prefer wax candles over olive oil.
Perhaps this idea of being brighter is just Rabba's explanation, but the real reason is unknown, and Rabbi Yehoshua ben Levi was thinking in terms of the fact that it was that oil which was involved in the nes of the pach shemen. Perhaps, but nowhere is that stated in the gemara, and furthermore, his related statement about ink belies that, making it more plausible that he is dealing with practical properties of the oil.
Not that I think that people lighting oil are acting incorrectly. Just that what is considered min hamuvchar should switch.
Aluminum Wick Holders
The alternative to floating wicks are standing wicks, using metal wick holders. Floating wicks float on the surface of the oil, and so drop lower and lower in the cup as the oil is consumed. A standing wick has a base at the bottom of the cup and extends to over the top of the cup. The wick seems encased in a metal sheath, such that only the portion of wick coming out of the metal will burn, but meanwhile it draws oil from the bottom. Thus, the flame stays in place over the surface of the cup, rather that getting lower and lower as the oil is consumed. This would seem preferable to floating wicks.
Perhaps it would also be preferable to wax candles, for the Mishna Berura's reason of the nes having been with shemen zayit. I am not so convinced that this is so, since the nes shemen was not mentioned by the gemara, and our only consideration should be respective brightness.
However, I would consider the following important. Rabba initially preferred poppy-seed oil because of its duration, but then switched to preferring olive oil, based on Rabbi Yehoshua ben Levi's statement and giving the reason that it burns brighter. It is quite possible that, given two fuels that burn with equivalent brightness, duration would once again become a reason for preference.
Also, I don't know whether to trust my own eyes. I think wax burns a bit brighter, or maybe equally brightly, even when the flame is on the surface, but perhaps I am incorrect in this regard. I also would need to compare these standing wicks side by side with wax candles.
I've also seen these in the $25 to $30 sets you can pick up in Judaica stores, which have the oil already in it. In terms of the prefabricated sets, some have said that the flames on these are not to good. However, Rabbi Gil Student notes in a comment in the comment section of his blog, Hirhurim:
As to the flame on these not being too good, that's only if you don't know the trick. You have to pull the wicks out a bit so that there is a good 1/4-1/2 inch of external wick that has been soaked with oil.There is also the apparent danger posed by one particular prefab set, as well as the difference in cost ($1 for a box of candles, $1 for floating wicks plus cost of oil, similar price for the standing wicks.)
The Eighth Day of Chanukka
One possible problem with using candles rather than oil lamps is that on the last days of Chanukka, due to the heat coming from the other candles, the candles might not burn the required half hour. This is a perception that has some basis in reality.
Specifically, it is a problem at Yeshiva University (YU) where, due to fire hazard concerns, they request that everyone light the Chanukka menorah in a common area (e.g. by the entrance of Rubin Hall, or of Morgenstern Hall), rather than in individual rooms. This common area is a (figurative) furnace, because of the hundreds and hundreds of candles (and oil lamps) burning in close proximity.
However, when we lit Meir's wax-candle menorah on the eighth night (which was Shabbat Chanukka) for chinuch purposes, all the candles lasted at least 35 minutes (and the last of them went out at about the 45 minute mark.) So, assuming the surrounding area is not too hot, candles should be fine for even the eighth night (assuming it is not Shabbat).
There are also practical measures one can take to make the candles last longer, the same as we do for Shabbat Chanukka: Use bigger or longer candles, freeze the candles, or move your menorah and light at a distance from other menorahs.
What if someone lights close to your menorah afterwards and so it ends up not lasting 30 minutes. I would think it would be no worse than if someone blew them out, since hadlaka oseh mitzvah? Indeed, perhaps one can even argue that within a single menorah, for the first few candles lit, before the final candles are lit.
Shabbat Chanukka
Shabbat Chanukka is another difficult situation when using candles rather than oil, since the Chanukka candles need to be lit before Shabbat candles and need to last 30 minutes past nightfall, rather than just 30 minutes.
However, there are solutions to this problem: Use larger/longer candles, and it can't hurt to freeze the candles as well.