I'm not an Xbox 360 developer, but AFAIK it is indeed a hardware unit. However it only does one thing: it generates domain coordinates from your control points. Your vertex shader still has to perform the extra work of calculating actual positions for the tessellated vertices, and also any displacement mapping if you're doing that. Plus if you want to do skinning you can't just skin the control points like you can in DX11, which means you instead have to apply skinning for each tessellated vertex. The domain coordinates aren't stored in memory so you don't get extra memory overhead, I'd imagine it's mostly extra shader overhead.
There's also the more important issue, which is that using it for any geometry outside of terrain would typically require big changes in the art/tool pipeline.