Acharei Mot #1:

Earlier, in parashat Shemini, I suggested that the cause of Nadav and Avihu's death was the same as that of Korach's rebellious Edah. Both went into the kodesh with incense in their pans, and both were killed by a Divine fire from before Hashem. Indeed, I interpreted Moshe's consolation to Aharon as explaining the cause for their death - בִּקְרֹבַי אֶקָּדֵשׁ, "Through them that are nigh unto Me I will be sanctified", that is, only through Aharon was the day's service to be done. Thus, Hashem chose Aharon to serve him from amongst Korach's Edah and from two of his sons.

However, the opening Midrash of parashat Acharei Mot basically rejects my suggestion. Rabbi Shimon cites the verse from Kohelet (Ecclesiastes) 9:2

הַכֹּל כַּאֲשֶׁר לַכֹּל, מִקְרֶה אֶחָד לַצַּדִּיק וְלָרָשָׁע לַטּוֹב וְלַטָּהוֹר וְלַטָּמֵא, וְלַזֹּבֵחַ, וְלַאֲשֶׁר אֵינֶנּוּ זֹבֵחַ: כַּטּוֹב, כַּחֹטֶא--הַנִּשְׁבָּע, כַּאֲשֶׁר שְׁבוּעָה יָרֵא.
All things come alike to all; there is one event to the righteous and to the wicked; to the good and to the clean and to the unclean; to him that sacrificeth and to him that sacrificeth not; as is the good, so is the sinner, and he that sweareth, as he that feareth an oath.

It is quotes like this that make you understand why Chazal wanted to be gonez Sefer Kohelet! It seems to deny fair judgement before God, since the same thing happens you whether you do good or bad. Unless he refers to life in this world, with punishment/reward in the world to come. Yet he seems to deny this in pasuk 5, when he writes:

כִּי הַחַיִּים יוֹדְעִים, שֶׁיָּמֻתוּ; וְהַמֵּתִים אֵינָם יוֹדְעִים מְאוּמָה, וְאֵין-עוֹד לָהֶם שָׂכָר--כִּי נִשְׁכַּח, זִכְרָם.
For the living know that they shall die; but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten.

I am not going to digress into a discussion of life after death and reward and punishment. The matter I focus on here is the drasha R Shimon makes of the first pasuk.

R Shimon parses each phrase and shows how each refers to a set of tzadikim and reshaim, who had the same end. The idea is that you cannot determine whether a person is righteous or not on the basis of their end, since often a tzadik and rasha have the same.

(Note for each of these identifications of people with appelations, the midrash cites prooftexts.)

לַצַּדִּיק = Noach
וְלָרָשָׁע = Pharoah Necho

Noach was injured by a lion in the ark, and made lame. Pharoah Necho (who killed King Yoshiyahu) took King Shlomo's mechanical throne, which had a security system built in. For Shlomo, the mechanical animals on the throne helped him ascend in honor, while for Pharoah Necho who did not know how to operate it, a lion on the throne made him lame.

Thus the tzadik and the rasha had the same thing happen to them.

לַטּוֹב = Moshe
וְלַטָּהוֹר = Aharon
וְלַטָּמֵא = the 10 evil spies

All three did not enter the Land of Israel

וְלַזֹּבֵחַ = Yoshiyahu
וְלַאֲשֶׁר אֵינֶנּוּ זֹבֵחַ = Achav

Yoshiyahu is described in Divrei Hayamim 2 as slaughtering animals for the populace. Achav is described as doing away with sacrifices.

Both died via arrows.

כַּטּוֹב = King David
כַּחֹטֶא = Nevuchadnezar

King David helped built the Temple and ruled for 40 years, and Nevuchadnezzar destroyed the Temple and ruled for 40 years.

הַנִּשְׁבָּע = King Tzidkiyahu
כַּאֲשֶׁר שְׁבוּעָה יָרֵא = Shimshon

Here this is interesting because presumably the one who swears is doing something bad, and so bad and good are reversed in order.

Tzidkayhu swore to Nevuchadnezar and broke his oath, and Shimshon put himself into others hands once they swore to him (Shoftim 15:12) so he beleived that they would not break their oaths.

Both died with their eyes poked out.

Alternatively, מִקְרֶה אֶחָד, the same happening, refers to Nadav and Avihu vs. Korach's Edah.

לַצַּדִּיק = Nadav and Avihu
וְלָרָשָׁע = Korach's Edah

Korach's Edah went to bring near incense for Machloket (dispute) and Nadav and Avihu went not in dispute. Both were burnt.

Conclusion: This seems to directly imply that Nadav and Avihu did not commit the same sin as Korach's Edah.