Since you like JRPGs, I cannot recommend enough that you try Persona 3 FES and Persona 4. These two rank as my favorite games ever (tied for that title), in large part on the sheer strength of the writing. I cannot recommend them enough.
There's also Shin Megami Tensei: Nocturne, of the main series that the Persona titles spun off from. It's much less story-focused and more of a dungeon crawler, but has some interesting story concepts, and it's a damn challenging game. Great if you like turn-based combat and monster-based parties (Pokémon-esque in a very broad sense, but very different from that series).
The first two Disgaea games are available there, and are great tactical RPGs. The first has the better story I'd say, while the second improves the gameplay in several ways. Both are worth playing. Unless you're an obsessive completionist, in which case playing one of those may mean never playing another game again.
Dragon Quest 8 is another JRPG there, probably the most traditional-style one you'll find since consoles went 3D, and my personal favorite entry in that series.
The Devil May Cry and God of War series are mostly on the PS2 as well, and are both great action series. Devil May Cry 3 is probably my personal favorite action game of all. You may want to skip Devil May Cry 2 though - it's not bad per se, but the story is totally incoherent, and the gameplay actually a step backwards from the first.
You've got my top recommendation, Tales of Vesperia, already. After that I'd normally point to Bioware titles (Mass Effect, Dragon Age), but if you don't like WRPGs at all, you may not want to play them. (Personally, while I don't particularly like any other company's WRPGs, I do find Bioware's to be very good.) They're all available on the PS3 at this point as well anyway though.
Some games that aren't are Blue Dragon and Lost Odyssey, two JRPGs made by Mistwalker, the company founded by the original creator of Final Fantasy. Blue Dragon is more in the style of Dragon Quest, cartoony and with a fairly straightforward fantasy plot, but has some very fun combat (although it's easy to break the game by the end due to the nature of its multi-classing system). Lost Odyssey meanwhile is basically a Final Fantasy game - you could seriously slap the name "Final Fantasy 15" on it and most people wouldn't bat an eye, except to ask why some of the spell names have changed. And honestly, I think it's better than the actual Final Fantasy games I've played (though to be fair, I don't have that high of an opinion of most of the Final Fantasy games I've played).
360 & PS3:
There's plenty of fighting games to go around, including a new one that's a sequel to my above-mentioned favorite games ever, Persona 4 Arena. That, the BlazBlue series, and Marvel vs Capcom 3 are my personal favorites, but without knowing what kinds of fighting games you like I don't know that I can really give recommendations (beyond Persona 4 Arena if you play and enjoy Persona 3 and 4).
Batman: Arkham Asylum and Arkham City are available on both consoles, and are probably the best action/adventure titles outside of the Zelda series (even if, like me, you don't like Batman). Devil May Cry 4 is also available on both, and while not as good as the third game in the series, it's still a pretty good action game in its own right.
I can't help so much on system models and whatnot, nor on PS3 exclusives (I could list those that I have an interest in, but since I haven't played them due to not having the system, I technically can't recommend them*). but there's my top game recommendations as-is. You actually have fairly similar tastes to my own, so that worked out quite nicely.
*With one exception: Tales of Graces F, which I have, and played by borrowing my brother's PS3. It's good, but not as good as most of the others of the series that I've played (Symphonia, Abyss, Vesperia). The story is disappointing for that series. Gameplay has some very good changes though, which I think makes it worth a play. And it's not like the story is bad, just not as good as its predecessors.