I have a henry, the trusty bombproof little work horse BUT in the past had a Dyson and it was very impressive.

Personally I would think the Dyson has more sucking power and will lift the cat hair better than a Henry, he's a trusty little bugger but not as powerfull.

The first Dysons tended to have parts that broke, but then the second design (going back a few years) they had redesigned those flaws so guessing the latest versions will be pretty good all rounders.