Blu-Ray wins, hands down. HD-DVD is about the same as BR in terms of picture and audio quality, but BR still has some serious advantages.
The biggest of which is that Blu-Ray has 5 of the big studios as exclusive supporters: Sony, MGM, Lionsgate, Fox, and Disney. HD-DVD only has Universal, and pretty much everyone else makes movies for both formats. Blu-Ray will have a superior movie selection once the big titles start hitting. Also, Blu-Ray is supported by almost all PC makers except Toshiba, ensuring a nice speedy integration to computers. Also, they are currently the format of choice for all the big electronics manufacturers except for Toshiba and NEC. And of course, it's integrated into PS3, making it the only next-gen format to house game software.
However, let's just forget about the support BR has from corporations for a moment, and just look at some features it has the HD-DVD doesn't. First of all, Blu-Ray has a protective coat that is superior to that of HD-DVD. HD-DVD scratches just as easily as normal DVDs, but Blu-Ray is extremely scratch resistant, and even when it get scratched it seldom affects playback (they demonstrated this by scratching a name into a BR disc with a needle and could still play it.) Also, the discs hold more than HD-DVD and are expandable. Theoretically, you'll be able to have the entire Fellowship of the Ring Extended Edition plus the extras in full-HD quality on a single disc. On HD-DVD, it'd have to either be multiple discs, or start sacrificing features and quality.
For me, the descision was not a hard one, especially since I was buying PS3 anyway. My suggestion is that you wait until this fall, because the price war between Toshiba (HD-DVD) and the Blu-Ray manufacturers is really going to heat up. Blu-Ray players will probably be availible for as little as $299, and there is constant talk that Playstation 3 could have a pricedrop to as low as $449.