There are three factions in the game Aion, being the Elyos, Asmodian and NPC factions. Only the Eylos and the Asmodian are for the players to choose from. The two factions are against each other and killing between members of the same faction would hurt all participants. Games involving factions more than two usually tend to have in-faction problems, which each player should struggle to avoid for the benefit of the team.
Choosing one faction is important for one account only allows one character on a server. However if you wish, you could try two factions on two servers. This would help you a lot in getting familiar with the game of Aion.
The choosing of characters within one faction is equally important. You choose a certain character not because you like that class, but that you have a team to play in, and the balance between two teams is also very important.
In terms of skills, some difference exists between the two factions, but generally the game is in perfect balance.