MH Oldschool

Left horn:
Right horn:

why is there such a big difference?

Probably that horn was damaged in a battle and it overgrew? We know that Crimson Fatalis is way more violent than the Black one and it usually lives in places where other very strong monsters appear, such as Ingel Island with Akantor.

As far as I know, the horns in the early parts of the game also (as in MHW) directly affect the unique skills of Fatalis. My friends and I still subscribe to the theory that the horns of Crimson Fatalis are different because it is a contiguous subspecies between the Black and White Fatalis. We explain this by the fact that the horns of the White Fatalis are longer (more branched) than those of the Black one, and also the White Fatalis performs many long-range attacks with the dragon element, while the Black Fatalis still uses physical attacks more often along with light fire attacks. Another point in favor of this theory is the ability of Crimson Fatalis to cause a meteor shower. This attack has more in common with the White Fatalis, and the element of fire and some physical attacks are taken from the Black Fatalis.
Yes, in MHW, Black Fatalis is more revealed as a dragon that uses more fire attacks, but he still fights in melee a lot.

Coming back in the future to point out that the overgrown horns are also the exact ones that you can break on Black Dragon Fatalis.

MH2 also explicitly states that the Crimson Dragon you fight in that game is the same individual as the Black Dragon that you fought immediately prior.

Given this, to me, it seems obvious that they're his broken horns now regrown by means of the bioenergy in the volcano, but I'm sure there are some other interpretations.

Either way, the asymmetry is very striking.