What I find painful with the moonphase is that you have to set it when you let the watch in the box for a while...
You have to go to the Net, find the good site, then take a tooth pick and push till you find the right moonphase.
Two nice watches, but I would go for the 5980. For the originality of the mono counter, for its historical movement ( first automatic in house ), and don't worry too much about the thicker case, it is still very comfortable on the wrist.
Best,
Nicolas