Technically speaking, Blu-ray is superior. Take a look at wikipedia.
I'd say Blu-ray is winning the war right now, but the recent release of sub-$100 HD-DVD players is a crushing blow for Blu-ray on the consumer end. The fact that many online retailers sold Blu-ray players but not HD-DVD players for a long time is big. Also, the PS3 being Blu-ray is huge also...the PS2 helped make DVDs big and I think the PS3 will help make Blu-ray big.
I personally don't think either will ever be phased out. One might become much bigger over time but I can't see one just going away.
Right now the HD-DVD for under $100 deal is long gone so the prices are back up to the $200-$400 range for Blu-ray or HD-DVD. I'd personally go with Blu-ray based on the selection of titles I see in stores. The Playstation 3 is the best Blu-ray player on the market because it has a fucking next-gen gaming console built in with it.
