Originally Posted by icesoft
Dealer probably overtightened the pinion nut and put too much preload on the bearings. I've rebuilt a BMW diff, and they're not too bad at all, the hardest part is getting the bearing preload just right.
E32 diffs will fit an E34 with no problems (direct bolt in), the only thing to watch out for is the pinion flange, as there were two sizes of those used (depends on motor/trans combination). If you get the wrong one, your driveshaft won't bolt up to it. You can swap the flange, but you risk screwing up the bearing preload.
Going to 3.91 will make 1st gear very short, you'll probably be starting out in 2nd gear all the time with that diff. Fuel mileage will go down, acceleration will go up, top speed will remain the same or go down (depending on if you hit the rev limiter before the speed limiter with that gear).