I am on 6 acres, hilly, rough and quite a few trees. I have always divided the property up into "pasture" and "lawn" areas (though I don't have any livestock). 600ft of gravel drive to maintain and move snow off of, lots of wood chipping and loader work. I used a 60" rotary cutter to mow the 4 acre "pasture" areas a couple of times per year and a 72" RFM (rear finish mower) for the 2 acres of lawn around the house.
The original goal was to have a compact tractor to "do it all" so I bought the JD 2520 with the aforementioned rotary cutter and RFM, but it never really worked out that way. I always needed a lawn tractor to "cut in" around the buildings and trees, which wound up taking more time than actually mowing with the tractor.
A year ago, after becoming frustrated with the whole process, I bought a ZTR to mow the 2 acres of lawn and this has worked out well (except for the rough ride).
That being said, if I were in your situation (assuming you actually want to finish-mow all 6 acres) I would use the ZTR for trimming around the house and tight areas and get a CUT with a big RFM to cover the rest of the area. You can make really good time with CUT and RFM in wide-open areas without getting beaten up buy the bumps. I think this also makes sense because you probably need the tractor for other tasks such as drive maintenance.
If you want to cut down on your mowing time, you might consider letting some of the property grow and just cut it a couple of times/year with a rotary cutter. The good thing about buying the tractor and keeping the ZTR is you can keep your options open if you find you like one way better than the other.
Another good reason to keep the ZTR is for a back up mower in case the tractor is down for some reason.