The Dreamcast had a lot going for it - i MUCH preferred it to the PS2. Unfortunately a combination of Sega having burned customers and retailers with the 32X (another good and misunderstood system, but executed terribly), Sega having spent so much money on diversifying their product line up (at one stage they had the Master System, Game Gear, Megadrive, Mega CD, 32X, Saturn and Nomad all being sold at the the same time in some territories!) and so having little money left to advertise and promote the DC and, lastly, the hype surrounding the PS2, which is arguably still the most hyped release of hardware ever (remember the "PS2 Emotion Chip" hype? The "PS2 is powerful enough to be used to launch missiles" hype? The "PS2 will have real time graphics of the same quality as the Toy Story movie rendering" hype?).
To top it off, the smartest thing Sony did with the PS2 was to include a DVD rom in it making it, for a time, the most cost effective way of getting into the then new DVD standard.
The DC, on the other hand, had far better video output quality, colour quality and output options. The DC had 4 controller ports as standard, the very novel (at the time) VMU system, networking capability out of the box, a vastly superior GPU system (very efficient system with 4 times the texture memory of the PS2 and hardware prioritizing of rendering allowing it to only render visible object and ignoring those hidden behind other objects - again, very novel for the time) and superior ports to the PS2 versions of games in almost every case.
The DC was far easier to program for developers, had the option of using the hardware libraries or using the WinCE development environment (making porting of certain apps, utils and games much easier)... in short, other than the PS2 having the DVDrom (which was really not useful for gaming at the time, save for storing heaps of FMV) and a faster CPU (somewhat negated by the less efficient design of the PS2 and the DCs more efficient GPU) and more system RAM, the DC was the better system - arguably better GPU, far more texture RAM, easier to develop for, more controller ports, VMU system, superior video output and out of the box networking. Oh and the DC had far more interesting exclusives - the PS2 was pretty much the usual suspects.
The DC has some absolutely amazing games, and the first couple of generation of PS2 games were not a patch, visually at least, to their DC counterparts. Of course, the PS2 being so popular and having such a long lifespan, developers learned to work around its inefficiencies and really make it do backflips - compare the first generation PS2 games to games like God Of War 2.
It would be interesting to have seen what could have been squeezed out of the DC if it had lasted longer.
....but then I am a Sega fan, so you might want to take what I say with a pinch of salt.
