I'm gonna completely buck the trend here and say a day at each minimum. At least that is what I have spent on the last half dozen trips and have been able to do a large majority of what I want. I really don't see how people still think that DHS and AK are a 1/2 day park. To catch all the shows and do most of the attractions isn't easily done. Doable, yes, but you really won't enjoy it. For instance, adding up the run times listed on Steve Soares site for DHS, it's 4 hours. That's a third of the day already (assuming 9A - 8P). Never mind walking around, waiting for the shows to start, waiting in line for seats. Toss in that, and eating, easily over half a day. And we still haven't done any rides or met any characters yet.
The only way I can see people doing them in a half day is if they write off attractions and don't go on them. In that case, you may be able to do it in half a day. But why?
Additional days? Always helpful. But it depends on what you want to do. If you like thrill rides, then you may be better off with a second day at DHS. Or if you are studying to be a zoologist, then AK. If I have the luxury I plan those days as it comes. If it rained one day at AK, you really would need a second, while rain at Epcot is usually minimal downtime.