dreamcast just had windows ce support, which basically no dev used because performance sucked, and it wasnt even built into the console.
well, 79 games used it out of 619. that's around 13% and included games made by Sega lol
xbox had a pretty strong sega library, and the duke controller kinda looks like an even chunkier dreamcast controller... but thats about it.
the original design concept for the controller had a VMU slot. the final controller still had the 2 memory card/expansion slot design of the dreamcast.
the Xbox copied the button labels of the Dreamcast (but changed the colors around to be a bit more sensical).
Sega was also in talks with Microsoft about making the Xbox backwards compatible with the Dreamcast, but that ultimately fell through because Sega wanted online compatibility, and Microsoft didn't want a split online service, where Dreamcast games ran on a free one, while they had Xbox Live in the works.
the xbox doesnt resemble a console sega would make, and the hardware's not a continuation of the dreamcast's--using a pentiumIII is very MS, not sega.
the Sega Chihiro (2002)
this baby ran, among others: House of the Dead 3, Virtua Cop 3, and a bunch of gundam games.
you can mod an Xbox to run Chihiro games. you need to solder in 128MB RAM and flash the bios of it tho.
also, the Dreamcast almost had a Voodoo 2 GPU. they ultimately chose an NEC GPU, but the Dreamcast almost had what was a popular PC GPU of the time.
and the PowerVR GPU it ended up with was also not really proprietary, just slightly modified, and had a PC equivalent part.
here's a Review of the PC card:
https://vintage3d.org/neon.php#sthash.1mxjkh7P.dpbs
DirectX 6 compatible! only 2 DirectX versions behind the Xbox!
so the Dreamcast was absolutely the closest in terms of hardware design to the Xbox of any console in the late 90s and early 2000s. hence Microsoft creating Windows CE for easy PC ports... as it did use relatively mainstream hardware that had DirectX API compatibility, just like the Xbox