It's hard to tell now, but it'll be a niche product once it initally releases. Both formats have their pros and cons. Oh and, Blu-Ray and HD-DVD are jointly released formats meaning no one company made it themselves.
Blu-Ray has great storage space, but it's expensive, disc and drive. Panasonic just released their second desktop Blu-Ray drive maybe a month ago and it cost $900. Expect PS3 games and movies to get a 10%-20% increase in price due it it's different (and expensive) manufacturing process. Paradox, Blu-Ray isn't backwards compatible with ANY current format because it doesn't share any similarities and is made completely different than DVD's or CD's. As for reading discs of different formats, that won't be hard, but you just won't see any Blu-Ray/DVD/CD hybrid discs.
HD-DVD's may have smaller storage space, but it's initial costs will be cheaper. This is due to it's manfacturing process which is very similar to the DVD, allowing it to be mass produced very quickly. One advantage HD-DVD holds is it's similarity with DVD, which allows hybrid HD-DVD/DVD discs to be made. That would be good because you could watch a certain movie in current DVD format, but once HD-DVD drives drop in price you can just flip the disc over and view the same movie, but High-Definition.
As for which format will fail, it's way too early to tell. All I know is that Blu-Ray's biggest backer (Sony), hasn't had the greatest track record with media storage formats. Remember the battle between Betamax and VHS? Betamax was big, and unweildy, which prompted people to buy VHS instead due to it's size and attractive price. It was cheaper because it's mechanism wasn't as complex as Betamax's, which meant production was easily done in mass quantities. Let's see...the MiniDisc? The MiniDisc hasn't had the greatest sales ever.
Initally released as a replacement for analog Cassette tapes, it didn't sell as well in the US and Europe, probably because the Cassette was too entrenched at the time. MiniDiscs are still around, but not widely used, partly because of popularity of CD's, and Flash-based and HDD-based MP3 players. Not as big of a failure as Betamax was, but it was still a failure. Hmmm, then there is the UMD! Haha, oh man, I remember when the PSP first launched, Sony hyped up the UMD to be the next biggest in movie storage and content, now it's lost several movie studios that used to support it, like Warner Bros. Recently, sales for the UMD have dropped slowly in movies. In games, I wouldn't expect it to drop much because to play games it uses UMD anyways. It's so funny though, too see Sony hype up the UMD format so much only to see it slowly fade away.
That's why I personally don't like Sony. All they do is hype and when that product finally comes out, they drop the bomb and give you shit instead. Oh and they need to improve in the creativity and originality department too. Either way, only time will tell which next-generation media format will win.