I have a 2 Xbox 360's, a PS3 and a Wii on the console side of our gaming setup.
If you did not already have a Blu-Ray player, I think the PS3 is in the running and maybe surging to the top. But as you do already have a Blu-Ray player, the clear choice is the 360. The 360 has a far larger library of games, far better DLC, better multiplayer live service (note: but it costs $$) and with Natal coming, a long 2-3 year upgrade path where the 360 will continue to be THE major game console that plays all the new Triple A games.
FWIW, the 360 in the living room easily sees the most use in our home. The PS3 is principally used as media server/Blu-Ray player and DVD player. I have about 20 games for the PS3, but three times that number for the 360. (very large library of used games is a big selling point for the 360, imo). The Wii is essentially ignored, even by my four year old. We have a dozen games for it, but we might as well not have any. It's used sporadically maybe once every six months? Something like that. The Wii was a waste of money in my house.
In general, the PS3 is used for games in my home too, but not as much as the 360. Because the DLC and online play is far more robust on the 360 than on the PS3, it is rare that I will ever pick up a game for the PS3 that is also available for the 360. Usually, the PS3 version of a game gets less of the developer's attention - and so it is the inferior product. That's a software issue, not a hardware issue. On the hardware side, the PS3 is a more capable platform. But that advantage is rarely seen in practice. In practice, it's just the opposite by the time a game is released.
I like having both major adult aimed consoles (and the Wii is certainly not aimed at adult gamers) and I would urge anyone to get both a 360 and a PS3 if they can. But If you can afford only one, the Blu-Ray is a big selling point for the PS3. Once that issue is off the table - the advantage to the 360 as a better overall gaming machine with a larger library of games is pretty clear, imo.
Which does not mean that PS3 is not the more capable machine, hardware wise. It is, in fact, a better and more capable platform. But in the real world, the major games are made for both consoles and so any advantages that might go to the PS3's technical edge are rarely, in practice, seen in any game except for exclusive PS3 titles (MGS4 is the best example, LBP and Valkyria Chronicles are other good examples).
Meanwhile, amongst games that are produced for both consoles, (and that is far and away most games in the marketplace), the 360 has a larger market share with more robust DLC, so more of the developer's time and money is spent on the 360 version. The 360 is simply where the most money is to developers. (Note: Notwithstanding this sweeping generalization, Dragon Age appears to play more smoothly and looks better on the PS3 than it does on the 360.)
By the way, my money is on Natal. I think Natal is going to be such a hit for the 360, that the 360 is going to totally capture all momentum in the marketplace from the Wii in the later half of 2010 and all of 2011.
Final result, the 360 is a better overall game console than the PS3 where the rubber meets the road in terms of how it is actually used, even though the PS3 is a more capable machine in terms of hardware potential right now. But with Natal coming in 2010, the choice is clear and the 360 is the winner.