I am going to list a few advantages for both formats:

Blu-Ray has more studio support. Deciding on a player might depend on the movies you want to watch.
Blu-Ray has more hardware support. Toshiba is the only manufacturer making HD DVD players at the moment. But an Onkyo HD DVD player should be available soon.
Picture quality is about even, despite what some people might say otherwise.
Audio quality is about the same unless one format uses a codec not available on the other format.
Disc capacity-
Now, the Blu-Ray camp will preach to you about Blu-Ray being better because their discs can hold 50 gigs vs. HD's 30 gigs. However, HD seems to offer a lot more features and interactivity that BD can't. In fact, I haven't seen a single example of BD using all of that extra space to its full capacity. If a multiple disc movie or box set is released on both formats they always have the same number of discs.
Cost of players-
Price of standalone players are much cheaper and you get much more for that lower price with the HD DVD players.
Features-
Better interactivity that is available with ALL HD DVD players because they are mandatory from the start. BD players sold now will not be able to do everything that the format will/could provide because the BDA decided to create 4 different profiles of players (3 video/1 audio). Let's face it, BD was forced to release their players before the full specs were in place. And I'm guessing a lot of Blu-Ray consumers have no idea their player might be outdated soon. There is even talk of a lawsuit:
[Link: tinyurl.com]

The companies backing BD are also some of the biggest receiver companies and they seem to have created the BD format to force people to upgrade receivers that work fine now just to hear the new HD audio formats.
You can say that it is not a fair comparison comparing the PS3 to a HD DVD stand alone player, but that contradicts with what most are saying. They are saying that the PS3 Is the best BD player option right now. People are saying it is as good with PQ as the other BD players. It also has the best chance to not be a doorstop when the next BD Profile1.1 & 2.0 BD players come out. Not only that, but without the decoders the current BD players will NEVER be able to play those HD audio formats because they do not have HDMI 1.3 either.
My thoughts on Sony-
I really never liked Sony due to the FACT that they always want to corner the market with alienated products. Blu-Ray for one is really a great product just as HD DVD is. But Sony should have went with Toshiba & the DVD Forum to work hard with HD DVD, but they chose to go against it and forced the industry into another stupid Format War. Did Microsoft force gamers to buy an HD DVD player with the Xbox? No. Did Sony force gamers to buy a Blu-Ray player with the PS3? Yes.
My thoughts on the format war-
I really have no idea if one format will prevail over the other. And nobody else does either. Even though some people THINK they know.
Final thought-
There is a possibility both formats will fail.