I've run both 820s and 1020s. Personally I think 1020s are way overrated and over priced, but the problem is that 820s are getting very old and good ones are getting really hard to find. 820s are very well designed heads, and the flex system and AHHC system is much better. The problem is that to get them to cut low you have to stand them on their nose (tip your feeder face all the way forward.) There is a gentleman in Illinois who modifies the cutterbar supports to tip the whole sickle down, then they really shave. Also, on the AHHC linkage tubes on the rear side of the header, they will pack full of dirt, limiting your flex travel, that is a very common problem.
1020s cut a little lower out of the box, but you still have to stand them on their nose as well. And the short skid pads and stupid leaf springs are a very cheesy deal, IMO. Also on a 1020 you get a bigger auger and usually fore/aft.
Both are decent heads if properly set up and adjusted. You just gotta decide how much $$ you want to spend. Around here I've seen 15'ers go for more than 20s.