If I were you I'd go PS3, especially at this stage in the console lifecycle. The Xbox360 is really being hampered by it's older tech DVD drive and processor while the PS3 is really coming into it's own and is much more future proof.
Sony Online, makers of everquest, has announced that all of it's future MMOs are being released on console also (PS3/PC exclusives) So as well as the current RPG line-up PS3 users will also have a number of MMOs to choose from.
DC Universe Online
FFXIV (ps3 only for a period of time if not forever)
The Agency
Are all due to come this year or early next year and more in the works. Both Microsoft and Sony are renownd for giving MMO makers a hard time making games for their consoles (hence no official announcement on FFXIV 360 yet), but since Sony has it's own MMO branch making numerous games and free online it is more likely to have a better selection and be more open to MMOs in the near future.
Don't forget also that the PS3 is japan's main console so it's more likely to get JRPGs developed for it, though microsoft did do a big push to get more on their console.
PS3 has more RPG games I can think of, and for fighters I really hate using the 360 pad compared to the PS3 pad, I got tekken on the 360 because it was cheap and quite regret it. USB controllers do work quite well with the PS3, I've not had one that doesn't work yet. If you've got a PS2 arcade stick you can buy a cheap converter and plug your PS2 pads into your PS3!
I used to advise friends to get a 360 because of the price, but now the PS3 is significantly cheaper once you add in having to buy wi-fi, a hard drive and xbox live subscription for the 360.
End of the day the PS3 is the better, more future proof hardware and is well worth the purchase. You won't miss out on much, if anything, not owning a 360 as the best RPGS and Fighters are multiplatform, but the way exclusives are going you're more likely to get exclusive FPSs on the 360 and a diverse range of games on the PS3, so getting a PS3 the only games you'll not be able to get will most likely be shooters and action games.
Edit: Just to add I think you might be pleasantly suprised with shooters nowadays. I only got my first latest-gen console the christmas before last and was pretty much the same as you, hated shooters and loved RPGs. I got killzone 2 and found myself quite hooked on levelling my character up (most fps have RPG-like levelling systems to gain more guns/classes) whilst shouting at the screen blasting other players and getting objectives done! Single player is still pretty much the same old thing though.
Whatever system you get I'd recommend Dragon Age: Origins too, great RPG!
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