Heya!
I don't play other shards (except a little bit of action with CHSY guild on Europa) so I don't know what other shards have for PvP. Chessy, however, has a pretty lively PvP scene. It's pretty rare that you can't find a fight (especially if you're an OJ or red). As for guilds on the shard, you got P@IN (TB), UM@D (SL), DOTA (Min), OF (Min), and LD (COM). None of the factions guilds are particularly more powerful than the others. You can usually find 4-6 of em if they're on in force. P@!N just split, so I don't think they'll be able to sport their 8+ anymore like they used to.
Non factions, you have GS which blues itself up at the gate to gank reds, PITS which is a blue spawning guild, and RBG which is a blue spawning guild. Currently there aren't any more major active guilds as far as I can tell. It seems that OATH (blue spawn guild) and TKO (non-faction pvp guild) have disappeared from fel. UHOH (faction pvp guild) is out playing other games but might show back up. Lox tends to read these boards from time to time.
I think Chessy has a good pvp community. It's not super crowded (if you want that, go to atlantic) but there is plenty of fighting to be had and guilds to join up with if you want.