The brush cutter needs more horsepower...that's a fact. They generally weight about 200 lbs. more the same sized finishing mower.
Of course, the intended purpose of the cutter is to work in areas that have tall grasses or brush...that would tear a finishing mower up pretty quick.
The rule of thumb I've read on TBN (and my dealer concurs) is 5 HP per foot of cutter width. Now, I've never heard it expressed as PTO HP or Engine Gross HP.
As far as finishing mowers...never hear any specific requirements, other then that which is recommended by the implement manufacturer.
That said...I run a 5' cutter through moderate to heavy brush (and saplings) with a 24 PTO HP Deere 790. That's 4.8 PTO HP per foot and it works mighty fine. However, I used that same 5' cutter behind a Deere 670 (16.5 PTO HP) which also did fine. That's 3.3 PTO HP per foot.
The 790 does handle the work better, but the 670 did a heck of a job. That cutter, per Land Pride, should be ran behind a 20 HP (minimum) tractor. Land Pride doesn't specify PTO or Gross HP, but I'm assuming they mean PTO HP.
As far as finishing mowers...I figure if the PTO can pick it up, the tractor can run it. I'm using a 5' mower currently. I could easily run a 6' mower...I'd even consider a 7" mower if it didn't overload the 3PH capacity. Of course, I don't have the $$$ for a bigger mower, but I know the tractor can handle more then I've got now.