Which faction is best to play against elves? Can Mages be formidable opponents for them?

Dwarves were specifically designed to counter Sylvan. Archers have a hard time against them, and that's the elves' biggest advantage.
Problems might arise with Necropolis, as they have Darkness and Sorcery heavily developed from the very beginning. So, even if you manage to upgrade Light and get Antimagic, you might simply not have enough time to remove Berserk and end up killing yourself...
Dark Elves are difficult for everyone...
Orcs have now appeared. I haven't played as Elves against Orcs yet, but I think it should also be difficult.