Assassins on Elyos can dodge 4-5 attacks&spells, Asmodian can dodge 3, but they have some lifeleech effects on some of their strong nukes.
Rangers had differences, but these were changed because they caused some balance issues, however they have different graphics on the same skills.
Templars/Gladiators on Asmodian side deal more damage because of their brutish style, they deal more damage on some abilities and regenerate hp to 50% of damage done.
Sorcerers/Spiritmasters
Asmodian Sorcerers obtain 50% Magic casting speed vs 500M.Boost (Both have the base versions, 300Mboost and 25% cast speed)
Spiritmasters get a different ultimate pet, Asmodians get Fire/Earth and Elyos get Water/Air - basically, you get the abilities of both pets in one and some special ones.
Clerics&Chanters don't really get anything special that I know off, I could be mistaken - Do your research!
There are some minor differences, the Asmodians have glowing eyes in combat, they also have claws and manes which adds some to the cool factor, they also have their darker skin and environments, where Elyos have the angelic feeling and pretty environments.
The wings are different as well, I do believe that the Asmodian ones look cooler, but some prefer the "plate" Elyos ones!
c/p van legion forum