Sega fucked up big time. Not with marketting, not with rival companies. Remember, the Dreamcast was out what? a year or two before PS2? PS2 didn't crush it, PS2 simply pulled the plug on a dying specimen.
Sega's fuck up with Dreamcast? First, they used Standard Compact Discs for their game format. Problem with that? Easy as hell to copy. PSX had that same problem but that brings me to point number two. Copy Protection! PSX -had- this. Granted, it was Modchippable, but that was a relatively unknown and hard to access feature. Dreamcast however didn't require a Modchip! All you needed were the right images (with the Copy-Protection overwrite frontend) or a simple boot disc.
Dreamcast couldn't sell games, nobody wanted to develop for it, and it died off. The games that were on Dreamcast were some of the best. Nobody can deny that, aside from the poor storyline turns and almost cinematic gameplay, Sonic Adventure was a fucking fun game.