Dreamcast was on it's way out, the company had exhausted too many financial resources and didn't have enough third-party support.
Xbox was MS's first attempt at a console, a new contendor released with limited third-party support and not too much of a line-up, released with much skeptisism everyone from Ken 'Kutaragi saying that it's going to be dead on arrival to news journalists the world over claiming it's some huge MS conspiracy. PS2 already had an install base and tons of titles people could recognize coming (MGS, FF, Tekken, etc etc) as well as the entire PS1 back catolouge.
Nintendo didn't provide as much competition as they should've because they lacked third party support that they lost with N64.
-----------------
Fast forward to the present, Xbox360 is out, they have 3rd party support from everyone I can think of. Name recognition, movie tie-ins with Peter Jackson (Halo), they've got new and promising franchises. They also have good hardware that many believe is comparable to the PS3's. Released earlier in the perfect season to get a fast install base and get some games sold. It's going to be cheaper when you consider that people can pick-up a Core system and get some gaming in... it could likely hit $200-250 within a year of release and see the install base skyrocket in time for the bigger game releases. They're pretty much in the complete opposite position that they were starting out with the original Xbox.
Revolution is coming out with an innovative controller and is attempting to reach the gamers of today and other people that might have not found games to be accesible to them. They'll likely launch at a lower price point than Xbox360 and be a lot cheaper than PS3, making their console less of a burdon to purchase if the right games are there at the right time.
All those factors cut into Sony's dominance, the previous gen was a wash for them because they were well established and started off with all of the games people wanted and hype beyond the imagination. I don't think they have as much going for them this time around and they face stiffer competition.