I hope we're not talking about cutting 1 acre of vegetation with either type of trimmer. The effective cutting width of either type of trimmer is probably less than a normal push mower, and it would take forever to cut 1 acre.
You can cover a surprising amount of territory swinging a brushcutter back and forth compared to pushing a walk behind through the same overgrown area. If we're talking about cutting 1 acre, however, then some kind of
self propelled brush cutter like a Gravely, high wheel yazoo, a DR or a Bachtold mower might be a better choice.
You might take a look at this post:
http://www.tractorbynet.com/forums/rural-living/206191-caught-my-first-mole-year-2.html#post2366214
Bachtold has or had a recall on some of their machines, but they were used quite a bit in rental places for many years.