It's always difficult to compare knives across a broad price range like that. I guess the best way to describe the difference is luxury or amenity appeal. I think most people, if they were to pick up a Mini-Grip, open it and close it a couple times, then do the same with the 960, would say the 960 feels like a much more precision-made, expensive tool. But will the 960 cut three times better, or three times longer? No. Plus the 960 seems to me like the kind of knife you'd really want to take care of if you got one, and you'd want to be careful of the anodizing ... while the nylon reinforced handle Mini-Grip is the kind of knife you wouldn't worry about much.
FWIW I'm mostly into practical, hard-working knives, but the 960 really stands out to me among knives in that price range that are intended to be a little bit luxurious. It's kind of like choosing between a Seiko dive watch and a TAG Heuer: the Seiko will probably keep time just as well and be just as rugged, but the TAG Heuer is intended to be something special that gives a sense of pride of ownership. Thinking of various production folders I'm familiar with in the $150-$200 price range, I can't think of any other as classy as the BM 960.
Dunno if that helps, hope it does.