Having owned both, I would chose the 936 hands down over the M816. HOWEVER, this is strictly from a coolness and more modern truck factor. The M936A2 (I have a thread on it) I am putting back together right now is a female dog of trying to find parts for. NO ONE who deals with your typical surplus vehicle parts will have parts for it espacially the A2 variant. I am having to find the actural manufactures of individual parts and calling them direct to find things like a u-joint and half the time they do not sell to individuals. The wiring on the M936's is a nightmare also. They're are more wires in a M936A2 then the stealth fighter (joking of course but theres a lot). My M816 was simple and reliable and parts are plentiful. The PTO setup on the M936 is TOTALLY different then the M816 also. While the PTOs on the M816 was transmission / shaft driven, the M936 is Transmission and transfer case hydraulic driven (the PTO that was missing off my transfer case alone was $800 and I still can't find the yoke for it).
Being an automatic and having air brakes is a big plus also in my book but that is because in LA I do not need to get a CDL to drive it (you may want to check your state regs on that one).
To recap, the M816 was a great truck and will do the same job as the M936, but having an automatic, air brakes, bigger cab, and CTIS w/ 8.3 cummins motor is a big plus in my book.
I am sure Bruce Kubu will chime in and agree with me. He could comment on the performance he having owned both.