I've got a Woods mower (BB840) (and recently sold an MD172, medium duty 6') I've also got a Bush Hog mower. (286) The Woods is 3 years old. Bush hog about 5 months. (I don't like a 7' single spindle 3-point mower in our rolling to rough ground. 6' a lot less scalping. All this has little to do with you question though.
The only light I can shed on the debate is a comparison of the brands. Both are each others single biggest source of competition (for sales) They mirror each other as best they can for model "features". Woods looks more streamlined. Bush Hog has a more rugged looking deck, with a not-so-rugged looking hitch.
Now the "side by side". I've owned 6' and 7' Woods medium duty. I've got Bush Hogs medium duty cutter. I sharpen blades the same way on both brands. I ran them on the same tractors, cutting the same fields. The Bush Hog has a better, cleaner "cut". Less grass/weeds popping back up the next day in tire tracks. Better shredding and scattering of clippings. Less chaff blowing out from under the front end (ending up on tractor and operator)
After using both brands enough to see what I needed to see, I'm looking to part company with the 7' Woods and buy an 8' or 10' Bush Hog (Most likely a pull-type if it's a 10'er)
Your results may vary, I'm convinced though.
For the record, quality, fit, parts availability (and price), and material used are almost identical between the 2 brands.