The first biggest thing in Sega Dreamcast's favor was that it came out 16 months before PS2. It was also $100 cheaper upon release, than the PS2.

From a development standpoint, the Sega Dreamcast was a much much MUCH easier platform to develop on, right out of the box. It's still a popular platform for homebrew game developers, beacuse it's a developer-friendly platform.

The PS2 was a much more difficult platform to develop on (especially compared to it's predecessor, the PSOne) for a long time, until Sony APIs and 3rd party development platforms started improving.

Sega's licensing policies and fees were also a lot more relaxed than Sony. However, Sony's PSOne was such a great success, that Sony was able to keep stronger 3rd party support than Sega, which resulted in a smaller library of games on Dreamcast. Sony had a larger marketing budget, and an already strong distribution channel. Sega's distribution was weak after Sega Saturn floundered for years in North America. Sony also had more influence over retailers, and was able to secure more shelf space for PS2 games (which became neccesary as their software library outpaced the Dreamcast 5:1).

Having worked on several projects both platforms, I can say that the PS2 did have a definite technological edge on the Dreamcast. It wasn't a monstrously huge difference, and one that should be expected considering the 16 month age difference and retail price difference (DC was $200 at launch, and PS2 was $300 at launch) between the two systems. Still, the PS2 was clearly a more powerful console, which is why it remained viable for 7 years, as of next March.

From a sheer number standpoint, here are the tehcnical differences:

Dreamcast CPU - 200 Mhz
PS2 CPU - 294 MHz (+ closely connected to system RAM)

Dreamcast GPU - 7.0 Million raw polygons/second
PS2 GPU - approx 20~50 Million ray polygons/second (debatable)

Dreamcast RAM & VRAM: 16MB & 8MB (100Mhz)
PS2 Ram & VRAM: 38MB shared (800MHz)

NOTE: I'm pulling these figures from memory, so they may not be exact, but should be close enough to illustrate the differences.

The Dreamcast was what it was, a less expensive and developer-friendly console that came out in 1999. The PS2 was a more expensive, and newer console. Even though they're part of the same generation (6th generation), they - as well as the anomalous Nintendo Gamecube and the late-breaking Xbox - are all pretty different platforms in many regards.

It's a lot like 7th generation of consoles... Xbox 360 is a modestly-powerful and lower-cost console that's very VERY easy to develop on. PS3 is technologically almost a whole generation ahead of itself, very expensive, and nearly impossible to develop on. And the Wii is a friendly anomaly, manufactured by Nintendo, who marches to a different drummer.