A hitch on the 3PT can rise up under the trailer, so you don't have to raise and lower the trailer to match the tractor. However, the 3PT probably does not have downforce, so a poorly balanced trailer can flip the hitch upward, which can go very bad if you're on a steep downhill.
A hitch on the drawbar requires you to lift and/or lower the trailer to match the tractor. It will handle best, though, if you are going far or fast.
A hitch on the FEL can rise up under the trailer, and has downforce to prevent tippy surprises. It makes backing up the trailer easier and more precise. But moving a big distance in the trailer's forward direction means backing up the tractor. I'm contemplating getting a small travel trailer and using the FEL hitch option to maneuver it around my woods for storage....