I have stayed at both Dromoland and Ashford and personally I found a huge difference. Ashford is far better. The service is excellent (among the best I've experienced) and staff were super friendly and welcoming. Granted the furnishing was not state of art (stayed pre-renovation) but was very comfortable. The extensive and very private grounds are fantastic, and it was great to escape from the outside world for a couple of days. Add to that the fact you are close to Galway and the Connemara region, which are among the most popular tourist attractions in Ireland.
Dromoland was good also, just not as good. The grounds are dominated by the golf course, so much harder to achieve that get away from it all experience. Just felt like another hotel rather than somewhere special.
Powerscourt would be a totally different experience to either of these, being a much more modern build. I have not stayed there, though the nearby Powerscourt gardens are worth a visit.
I would go back to Ashford in a heartbeat.