A few days ago I updated the page in my Horn Articles Online site that describes a pair of piston valved horns owned by ASU, an early Hawkes single horn that takes crooks and a Selmer double horn. Read the article for more information.
Having played a good bit on several different piston valved instruments I would say that they do have a faster action speaking generally compared to rotary valves. In the days of single horns piston valves were fairly common, but today they are quite rare. The best piston valved horn I ever tried (briefly) was a custom double descant horn by McCracken. A great horn but clearly one of a kind, with a much more comfortable, slanted action of the valves compared to the ASU instruments.
Why so few piston valve double horns? I suspect strongly that the main reason is because rotary valves just work better in terms of actually laying out the tubing arrangement for a double horn.