I also own both and am going to put my $0.02 in without reading any of the replies since they're all bias anyways.
Both have strengths and weaknesses, but it mostly comes down to usage.
For strictly gaming: Xbox 360 without a doubt.
Both systems have about equal performance in games and image quality. Very few games that appear on both platforms look noticeably better on either system. Now that you can install games to the 360 HD, the 360 is superior in this sense since you can install any game to the HD while some pS3 games don't install anything to the HD at all.
The 360 controller has the superior design and button layout. I can play for ten hours straight on the 360 and not know it. The PS3 controller reminds me every hour or so I need to take a break because my hands hurt.
The biggest advantage for 360: Xbox live
If you play games online religiously, the 360 and xbl is the only choice. Xbox live is so far and above he PSN that $4/month is a fuckin steal. I would pay Sony $10/month just to pretend to care about online gaming. The fact that PSN is free is nothing but a cop-out, a poor excuse for either being unable or unwilling to deliver a satisfying online experience. PS3 users just don't understand what it's like to have party system and most importantly *gasp* the ability to send voice messages in and outside of gameplay. I know, it sounds like witchcraft or some other heretic practice, but damn it's nice. XBL also has way more actual players and *gasp* most of them have mics! If I get into another ps3 game online and I am the only dousche bag with a mic, I am going flip out. A lot of it has to do with there being a lot more little kids that play on the PSN than xbox live. Mom and dad buy little johnny a ps3 because he wanted xbox, but this way they can watch bluray movies and don't have to pay for xbl. Well hell no they're not going to go out of their way to spend another $40 on a Bluetooth mic. The result? Me yelling profanity and insulting remarks to eveyone unchallenged.
For other than gaming usage: PS3 duh
If you like to pretend that your gaming console is this all in one l33t media center, don't waste your time with the xbox.
I'm glad the OP mentioned HDDVD because I still hold firm that both formats looked exactly the same. But since BD won, this is a huge advantage to PS3.
The other media center functions of the ps3 are there but extremely unremarkable.
I HATE that I can transfer files from PCs to the PS3 but not vice-versa. What a crock.
In the end, your PC is light years ahead of the PS3 as far as media center capabilities. So just get an xbox if all you do is game. Get the PS3 if you want the other stuff, but be prepared to sacrifice some enjoyment on the gaming side for it.