There are a lot of parallels that can be drawn from the much earlier VHS vs. Betamax competition, where there was a clear winner... But this time I don't think that's going to happen. Both sides have some pretty major players backing it, so I expect both will be around until such time that it's time for a new format.
It likely won't matter much. You'll be seeing more and more hybrid players that can handle either format, so you can just buy a movie and pop it in the player. Obviously PS3 games will likely be coming mostly on blu-ray discs, but who really cares that it's blu-ray? You care that the game plays on your PS3, and that's about it.
As for the PS3 catching on... I'm quite sure that once FFXIII is released, sales will pick up in a big way. But I also expect next year to be much better for the PS3, with Sony planning a pretty significant number of releases for the console. I forget the exact figure, but I think it was on the order of 200 new titles. Few people are willing to buy a very expensive game console that has a very limited selection of games.
Wil the PS3 catch on here in the US? Maybe many are waiting to see who will win the dvd format war bluray or hd. Anyone know how long the war will last?

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