I asked this same question of a racer here that has used both pretty extensively (he's one of those guys that has to test everything, I love him!).
Pirellis are stickier in general for similar conditions. The flip side of that is that they tend to break loose a little less predictably.
The Dunlops are a little less sticky, but more predictable.
The deciding factor for me (I'm not out to win championships) is that the Dunlops can take ~50+ heat cycles and barely change their grip characteristics. The Pirellis, even if you're relatively easy on tires and don't wear them out, start losing their grip ability after 15-20 heat cycles.
This is probably why jkv45 has the experience he does with Pirellis.