Well, maybe I'm the only person responding that owns both. I have an 8 year old Bad Boy Lightening Z which is very similar to the current Outlaw model. I recently acquired a lightly used Grasshopper 725K2 with power vac and dump from seat hopper.
I wanted a front mount when I bought the BB 8 years ago, but was not willing to cough up the significant amount of extra money. The BB has served very well. One of the attractive things about the BB was the ease of access to everything. Now that I have a front mount grasshopper I find it every bit as easy to access.
The BB is a very solid built machine. I can't think of any other mower with a deck fabricated from 1/4" plate. The spindles, pumps, motors and other mechanicals have been bullet proof. I have no reason to believe that the GH mechanicals are not equally stout.
The difference in the two is in the drivers seat. The GH does not have the top speed of the BB, but it makes up for it in maneuverability because of the front mount. The GH also seems to have more precise control, with the handles being more progressive in their operation. Part of the mowing I o is over rough ground and in uneven areas like the curved bottom of bar ditches. The GH lends itself better to this kind of work.
In my case my GH and BB are different in that the GH is a 61" while the BB is a 48". So, it should be no surprise that the BB being smaller and with no hopper to watch out for, is better in close quarters, but both of them are better suited for more open mowing than close quarters.
All this said, if I were forced to only have one of them, I would undoubtedly have to give up my beloved Bad Boy. I wish I could have bought the GH 8 years ago.
Larry