Sports games the 360/PS3 are essentially equal. Even online, I've never had issues finding games on the PSN/XBL. (Basketball, Hockey, Madden,etc).
Shooters (I would probably give the edge to the 360, but I prefer the shooters on the PS3). It essentially amounts to Kill Zone 2 / Resistance versus Halo 3 / Gears of War. You didn't specify first or third person shooters, So I'm guessing you kind of like them all. In which case, games like Uncharted Drakes Fortune, Warhawk , etc could all be added.
RPGs. While the 360 has had the more appealing lineup of RPGs thus far this generation. I'm not so sure I would turn my back to a Japanese made Sony console when it comes to RPGs. I foresee most RPGs on the 360 that the PS3 is missing to be migrated at some point to the PS3.
Other factors that I would say should play into your purchasing decision (Or would if I were you) :
Price. The 360 easily wins in this category in terms of entry point. It gives the ability to jump right into HD gaming with a low $200 price tag. Although, you should realize that a cheap entry point now will eventually lead to what appears to be a higher overall cost (When you factor in Xbox Live (Like $50 per year), Possible other needs Bigger Hard Drve, Battery recharger kit ($15), WiFi Adapter ($100). Which leads me to my next category.
Value. The PS3 I believe easily wins this category in terms of 'What you get in the box'. It's more expensive than the 360 but provides you with absolutely free online gaming which assuming you own the console and wish to play online for atleast a few years (Let's just say 3), would be around $120- $150 additional costs for the 360. The PS3 also has built in wireless/ethernet port. And lastly, the PS3 includes a Blu-Ray player.
Reliability. This may or may not be a big concern to you. Personally, I hate faulty hardware. A big concern with the 360 is the seeming ongoing issues (RROD, E74 errors etc). Microsoft has the extended warranty (Which is very nice), but for me personally it's not worth it. The PS3 is a far more reliable system, But like all hardware it too can break.
Upcoming game releases? Let's face it, a lot of buying a console is looking forward to newer, better games. Seeing where your console is going to be games wise in a few years is a good thing. While this is always in a state of constant flux and titles are being pushed forward, moved back, etc. Look at the upcoming game releases and decide for yourself which looks better. Most objective observers would say that the PS3 has a slightly-extremely (Depending on opinion) better lineup in the near future. Although realize that this could differ depending on your opinion and certainly many people might change their minds after E3 this summer.
All in all, Like most others have said it all is going to depend a lot on personal preference.
As for your decision? I think it plays out like this :
Game types you enjoy (Shooters, RPGs, Sports)? - Both systems provide an equally enjoyable experience. IMHO.
Price - The 360 simply gives you a lower entry cost, although it may result in a higher end cost depending on your usage. The 360 still provides a best price to someone on a budget.
Value - The PS3 simply gives you the most bang for your buck. Depending on your tastes though (Blu-Ray, Need for Wireless, etc), it may not be for you. Still the PS3 provides someone the most advanced piece of hardware package at a reasonable price.
Reliability - The PS3 simply is the more reliable system. Although the 360 has supposedly improved on this. Between RRODs and other issues (Many that aren't covered under warranties) it's easy to give the PS3 a nod. (For example, my 360s disc tray broke and wouldn't read discs anymore. In order to get it repaired, it would cost me $110 as it wasn't covered under the warranty).
Upcoming game releases? - This is where your opinion kicks in. Personally, I think the PS3 has a far better, more diverse, future lineup at this point and for the foreseeable future. (God of War III, Gran Turismo 5, Heavy Rain, Uncharted 2, MAG, New Ratchet and Clank, etc). But this category is the most personal opinion based one of the bunch. So just take a look yourself.
