pve characters can take part in pvp. pvp only characters are for pvp only. that's about all there is to it.
however, keep in mind you can create anything you've unlocked on your account on your pvp only characters, which means that unless you've spent 200k+ gold equiping your pve character, the pvp character will be superior.
I find PvP characters to be relatively easier to set up. Also, PvP characters have an advantage over PvE characters in that a PvP character may load an equipment template in seconds, whereas a PvE character must buy, equip, and enchant their armor piece by piece.
If you enter a match in random arenas, one team can consist of both pve characters and pvp-only characters. There are no separate districts/matches for the two character types.