Here's what I know...
I definately had a 2.83, the barcoded part sticker with the 2.83 designation was still on the original.
I definately installed a 3.15. Same sticker, different part number and 3.15 designation.
The diff is in huge supply without danger of running out at Pacific BMW. Mine was $440 after the $100 non refundable ('cause you can't turn in a 2.83 for a 3.15) core charge.
I am not half the mechanic that Larry is(see below): It took us from 9:00AM until 3:30PM to find the right tools and complete the install.
I did have to change the hubs from the old 2.83. I must have read the message below posted by Larry about a hundred times, but my buddy and I finally figured out how to remove them. (THANKS, LARRY!!)
And, there *is* an improvement, as others have noted around 3K, but I was expecting the same, off the line, tire screeching, pushrod type, Annie get your gun, Katie bar the door, wheel filling with smoke, off the line WAHOOOOO that others describe...
One of the hardest thing to find was the damn E14 star socket (for the axle bolts). I'm in AutoZone's corporate hometown (Memphis), and I couldn't find an E14 at ANY Zone. The other hardest thing was maneuvering BOTH of the diffs out and back into place. PITA!!
I also took two Mavica disks full of photographs to help anyone who might want to DIY this install. I am working of a web page that will detail and give complete instructions.
Back to the original intent of this message though, the same thing happened to me when I did the diff on my '75 2002. I upgraded to a LSD from an '81 320is, and thought I had lost tourque. Turns out that the diff driving both wheels 'softened' the effect of the tourque.
I called Pacific to make sure I hadn't been sold the M5 diff and I hadn't-- it's a different part number that they say won't work b/c of a different driveshaft on the M5's. I asked whether it was possible that I had a limited slip 3.15 to which they replied, 'No.'
Have you ever 'brake tourqued' your 540? You know, pressing on the brake while hitting the gas? I never did with the old diff, but with this one, in an effort to see WTF was going on, I tried it. BOTH wheels spin.. Why? Someone could help me out on that one. What happens to those of you with the 2.83's? One or two? (Oh yeah, take off the ASC)
What I need to know is whether or not a differential could be non limited slip, but have a different left hub:right hub ratio point (or something?) at which wheel stops spinning, sending all the drive power to the other. Like, if the two diffs were stuck in the mud at the driven wheels of each, would the non driven wheel (on solid pavement) of one diff 'try harder' than another?
Any gear heads out there?
If this is possible, it could answer why the car doesn't FEEL like anything has really happened on the butt dyno, but it will actually show up on the real thing. BTW, I didn't get to dyno the car for a before, but I'm hoping to do one with the 3.15 real soon.