Well, I have owned all 3 systems and currently own a PS3 and an Xbox 360. Until recently the 360 had an obvious advantage due to having a larger library of titles. Xbox Live is also decent for downloading episodes from TV series, movies, etc. However, in all fairness the Xbox is the most expensive, or at least it was for me. I bought the Elite, a year of Live, and of course most stuff on Live costs a nice amount of dough. I think Xbox has seen it's peek and a few titles like Alan Wake and Fable 2 will still be coming out this year. Past that it is up in the air.
PS3 is awesome as it has a built in Blu Ray player, the best Blu Ray player available mind you. PS3 sports firmware upgrades, you can throw Linux on it, upgrade the Hard Drive, memory cards from cameras, etc., stream multiple movie formats from your computer (easier than Xbox by far), and of course Blu Tooth accessories. The downside is the PS3's lack of exclusive content compared to it's competitors. However, this year and early next year is going to be a great year for the PS3. Not to mention the online stuff is free and constantly being improved.
The Wii was a novelty item for me and I can only play so long at one time. Since I have sold my Wii many other good games have come out. If I had the spare dough I would buy one again to play some of the good single player games, Wii fit, Mario kart, SSB, and Wii's new online service for downloadable modern games (Wii Ware). The Wii is just getting some pretty decent looking titles from 3rd party developers (The Conduit, Gyrostar). Don't forget some games will feel enhanced due to different a control scheme like Pro Evolution Soccer 2008 or Tiger Woods to an extent.
Well, if you want a system that is staple, but has constant expenses get the Xbox. If you want a system that has great potential, keeps improving, has a lot of other features, but has yet to have it's year with several near titles get the PS3. If you want some novelty feeling to your games and aren't too concerned about high def. graphics, but like the idea of playing with the family get the Wii.
Personally, since you are looking at a new 1080p LCD TV I would get a PS3 for your hard core needs, Blu Ray Player, and more high def. games. However, it would be a great compliment to have a Wii as well for it's shorter, more social oriented games. Keep in mind it does have some good single player games as well.
PM for any game recommendations or TV recommendations.