It was going to be a lose-lose situation, I'm afraid.
For a number of reasons:
-The Playstation brand in 90's was as strong as Nintendo;
-A big deal of loyal SEGA fans were pretty much upset that SEGA had abandoned it's Saturn console;
-As impressive as the Dreamcast was in those days, it had peaked as far as overall performance in 2001, just as the PS2 was still in it's early infancy, I can't remember the exact details, but I do remember at one point Tecmo saying that the Dreamcast was barely able to handle Dead Or Alive 2;
-Piracy, often cited as one of the easiest consoles to crack, till the PSP came along;
-Lack of DVD player, the Playstation 2 arrived at the right time just when people were moving away from Video-CD;
-SEGA not reaching the intended userbase, I don't think SEGA ever released the Dreamcast's actual sales numbers, that was telling;
-Major IPs that were made to be console sellers,but most of 'em underperformed;
-Not enough marketing, or rather effective marketing;
I could go on.