"What are the issues with tractors made after the post emissions technology?"
A big part of the emissions problems on tractors are actually caused by the operator. Either by not understanding exactly how these things work and how the tractor needs to be run to keep the DPF happy or by the dealers not teaching the owners how to properly run the tractors with DPF. Another big thing I suspect it happens a lot, is that people buy tractors too big for their application and can't simply put enough load on the engine to keep the DPF happy, however, this could be solved by going down the road every once in a while in the highest gear and RPM.
"Are they more troublesome?"
Maybe a little bit more, but mostly because these tractors do have a lot more electronics going on. And rodents are around, they can make a mess on the wiring.
"More complicated for the backyard mechanic? Lost their simplicity?"
Most are due to all the electronics going on, and specially ECUs that only the dealers can access those for diagnostics. So far I believe Branson is still the easiest tractor to work on as they retain the mechanical function as much as they can. The engine is still fully mechanical and so is the rest of the tractor. They only get the data logger for the DPF but that's pretty much a standalone unit and won't leave the tractor dead if something happens to it.