Messicks did a review of these SSQA style post hole diggers, it looks pretty awesome.
www.landpride.com
I've always heard 3 point mounted post hole diggers are not the greatest - but I've never used one.
Sounds like you've got a few main criteria:
1. Weight - not too heavy to rip lawns (or if it is heavy, you can use plywood)
2. Lift capacity - 1,600 lbs was mentioned
3. Post hole digger
4. Budget (this wasn't mentioned but I'll assume it matters)
I'm not an expert in fencing or tractors, but part of me thinks this is the wrong type of equipment for the job. In my mind I'm seeing a nice residential/suburban setting with a giant L4701 or MX Kubota trying to do fencing. Seems like it'd be clunky to maneuver around properties in addition to heavy and not built to be gentle on the ground.
What do fencing guys in the area normally use?
How often do you need to lift 1,600 lbs? Is that weekly? 1 time per year? That metric alone pushes you into a big tractor. It might not be a great idea to overbuy/oversize if it's a task you don't encounter that often.