Depends on a variety of preferences you may, or may not have.

All I can tell you which I believe offers the best in these departments.

X360:

RPG'S/Racing, FPS&TPS/RTS (Although this will always stay pc territory)

- Forza franchise is great and sees frequent releases
- Halo Wars is a great RTS
- Halo, Gears of War etc are great, but as you said, you are not really looking for shooters
- Mass Effect franchise is something you should not skip if you love RPG's

PS3:

Platformers/Action-Adventure games/"Hack&Slash"

- Ratchet & Clank franchise is a absolute must
- God of War franchise also an absolute must
- "Ico" HD collection is definitely worth looking at

Of course these are my personal opinions, and you may or may not agree with them, just trying to help you out, I personally prefer my X360.

Note:

Maybe it's best to wait untill after E3 & WiiU launch to check any possible price drops or game announcements.

well when you throw shooters out the window, and every third party game can be found on both systems, there's only one clear winner, and that's PS3.

i'd agree with Rol in some areas of his second post but you're looking to step out of the worlds of PC, and ninty.

Toughie. PS3 I'd say is better for platforming/action adventure exclusives but 360 I think is still better overall for RPG in terms of exclusives.

What about online? Is this important or something casual for you? If important 360 has slightly better online but it only really comes into it's own if you regularly play with same friends, etc. Otherwise PS3 offers pretty much the same experience if you simply play casually with strangers and there is no fee.

You know what, why not take a long, careful look at the true exclusives for each at the moment (including 360/PC exclusives as it sounds like your PC is not that powerful) - i.e. Gears, Left fo Dead, etc. on 360 or Uncharted, Ratchet & Clank, etc. on PS3 and decide which has more titles you are interested in.

Given most of the titles on each are the same 90% of the library is pretty much identical so you'd probably be best served deciding which exclusives appeal more.

Or think lateral and get a 3DS or Vita instead. Or wait a bit longer and get both after the price drops all the analysts seems to reckon are coming this year.

plenty

Retail:

Alan Wake

Crackdown

Kameo

Banjo Nuts and bolts

Mass Effect 1

Fable 2

Star Ocean

Lost Odyssey

XBLA:

Bastion

Shadow Complex

Limbo

Banjo 1 and 2

kingdom of kefflings and 

Ilo Milo

Trials HD

Splosion Man & MS splosion man

The Maw

Toy Soldiers & TS cold wars

DishWasher & Dishwasher 2

Crimson Alliance

For the library of games, the ps3 is the easy choice.

Yeah, I'm definetly getting the Mass Effect series - sooner or later. That's a given (as is Batman: Arkham-series)! I'm not quite familiar with Ratchet & Clank... And the only Ico game I've heard of is "Shadow of the Colosos" - that's in that series, right?!

Oh, yes, I forgot about them, but the Batman games are absolute gems!

Yep, SotC is part of the Ico collection (And arguably the best game of the 2)

Also, as kowenicki said, Alan Wake is a brilliant X360 game, it might be a bit niche and not for everyone's taste, but I loved it.

Online is not an issue for me: I couldn't care less! I'm not really that good at gaming, so I like to take it nice and slow ;)

I would get a 3DS - but they really have to redesign it first! And get a little bit more SW support...

When is this price cut coming? This summer? This fall?

I'd probably go for the PS3 but I'd lie if I said it was the obvious choice. I don't think you'd be disappointed in either of them so it all comes down to which one has the best exclusives to fit your needs.

Mass Effect I'm geeting, I'm just not sure if it'll be on the PC or a newly acquired 360... And Fable 2 I've played and enjoyed it! Is Alan Wake any good? Beside those I've mentioned here, I've never heard of any of them - well, almost anyways...