I actually feel like DC and Xbox have a very different vibe; DC was like an arcade machine squeezed into a console box while Xbox was a PC squeezed into a console box, and late 90s arcade gaming and 2000s PC gaming were quite different in feel and philosophy. Maybe that's just me.
On a literal level this is correct. Dreamcast hardware was used in Arcade machines as the Naomi board. Xbox used PC parts and the controller ports were USB 1.0 just with different connectors. You could splice USB cables with Xbox controllers to work on PC and many did. You have to understand tho. SEGA fans were homeless. MS had connections with SEGA from DC and had a lot of ties. It was the perfect place for SEGA fans to go to. Sony and Nintendo were seen as rivals/enemies for years.