Some consider Syntax the RP server, but that's really not necessarily the case.  There's RP on all 3 servers (though, for obvious reasons, you may not find people just standing around RPing at a hardline on Vector), but the style and content seems a little different on each.  If you're looking for a taste, I suggest checking out the Next Renessaince section for each server.  Not all RP is on display there as some players keep most of their RP in game, but it's a good start.

If you really can't decide, you can always start a character on each of the servers and travel over to the main population hotspots and experience each one yourself.

There's some RP on every server.

I'm not the judge of which has the most and I'm certainly not the judge on which is better, but I can direct you to some forum boards where a lot of RP happens

Vector

Recursion

Syntax 

And non-server specific

Hope that helps some and maybe get you started a little.

Also, generally speaking, Tabor West on Syntax is considered the "RP Hardline" and Camon Central for Recursion.