Sennadog
I haven't flown the DA20, but have logged time on the DV20.
The Katana couldn't be compared to the Piper range, especially the PA28 as it is a very different airframe/engine combination.
For instance, the Hoffman CS prop and Rotax engine gave sparking performance for 80HP and the handling/controls were much lighter.
The handling is not dissimilar to the Pup 100, although the Pup was probably a bit crisper (but I would say that wouldn't I), but the enduring memory for me was of a truly modern light aircraft, not a 50s throwback.
Hope this is of some use.