The older Woods mowers were rebadged Grasshoppers, but that marriage was over with several years ago. Having spent alot of time on Toro and Gravely mid mount commercial ZTR's, I bought a Grasshopper purely for the sole reason I always wanted one as I liked their design. I will say that hillside stability and traction is more an issue of tires than machine, but bar treads on a midmount and you have a stable traction hog mower. The Toro (bar tread tires) would go anywhere (except mud), and cut great, rode good. The Gravely (turf tires) cuts ok, rides like a log wagon, built like a tank. My Grasshopper (723K 52" deck) rides great, cuts awesome, traction suck but I have turf tires on it, bar treads will make a world of difference but mine was very lightly used with turfs on it, so I have gave them a chance and I hate them. I have a few hills and have learned how to attack them, but in general I would be happier and better off with bar treads.
If you are in the market I highly recommend Grasshopper, get the powerfold deck (mine doesn't have it, I am 31 in good shape and strength, the deck is a tad heavy to lift manually), get bar tread front tires, I would like a diesel because I have a diesel tank sitting at the house and have to haul gasoline. But I have no complaints on the 23 hp Kohler.
Oh yeah, when looking at Grasshopper front mounts you have 3 frame sizes, 600 series, 700 series, 900 series. The last two numbers of the model indicate hp, 723= 700 series 23 hp, 930= 900 series 30 hp. 900's are the big boys, 72" decks are the norm. 600's are small, 700's are the most popular line and are what you see most.