Summary: Compared to one who strikes them. According to R' Yonasan Eibeshitz, it is because the curser admits to Hashem's hashgacha, yet tries to bring Him into this evil. Or, because the striker can be excused, since striking is the fault of a person's animal soul.
Post: Rav Yonasan Eibeshitz writes on parashat Mishpatim:
"And one who strikes his father or mother, he shall surely die. And his death sentence is with strangulation. And this that it was more stringent with cursing than striking, for one who curses his father or mother is punished with stoning.
It seems that the reason is that at times, the striking is due to his thinking that the world runs in its set path, and Hashem does not direct the lower world. And if so, his punishment will not be as severe as the one who knows that Hashem directs, and even so, sins. And behold, for striking, there is to say that the one who does this thinks that Hashem does not direct, chas veshalom. But one who curses, he is the one who curses via the Divine Name, and if so, his intent is that Hashem should intercede in this. And so he admits to Hashem's direction, and requests that Hashem aid him in this evil. Perforce, his punishment is more severe.
Another plausible reason for why the penalty for cursing is more severe than that of striking is that the striking of one's father or mother, that is the act of an animal. For so does a calf, when it grows older, it hits the cow and does not sense whether it is its mother or not. And so too, a person has an animal soul, as the Zohar darshens upon the verse ויהי האדם לנפש חיה. And so, there is to the striker a bit of an excuse, for the animal soul within him caused this. But one who curses via the Name, this is not the act of an animal, but rather his Intelligent soul. And therefore, his punishment is more severe.
And therefore, the Torah interjects between the one who strikes his father or mother, and the one who curses, and writes between them וגונב נפש, to make a separation. Why is theft of a person more severe than the theft of an animal? For a person has an upper intellect, from the likeness of the Omnipresent. And one who sins in this, sins regarding this likeness. And so is the law regarding one who curses, for he casts his hand in his intellect, in likeness of the Omnipresent."
For more on the tripartite soul: the rational soul, the animal soul, and the vegetative soul, see here.