I'm pretty sure the USA M3 had a medium case 3.15LSD but I'm told the Euro M3 has a large case & I'm unsure of ratio. I think it's a 3.23. It should be on the diff somewhere, on a tag or label. If not, google it. I found too much contradictory info though. I'm thinking it a bit too low a ratio for your motor, but you'll get a bump in fuel economy and quieter highway running.
I found
this page about it, the US e36 is mechanically the same as the Euro e36 AFAIK. Should swap right over if you get the entire rear subframe in there. Since you're getting the whole rear end that won't be a problem.
If you don't understand a diff, here's the skinny: The ratio is the number of times the input shaft (off the tranny) will spin for every output revolution (to the wheels). So if you have a 4.1, you'll get one wheel rotation for every 4+ incoming. Great for little motors like ours, it's called a 'short' diff (because it runs out of revs quickly). The motor has a lot of mechanical advantage too, so it'll get the car moving faster. However, it'll eat more gas & run high RPMs on the highway.
As you cut that ratio down ("taller" diffs), each engine rpm gets you less advantage. So the car gets slower. The transmission output has to only turn three times for each wheel revolution though, so you'll get more top end and each gear will "last longer."
My e30 318i had an open 4.1. It went bad so I swapped in a 3.73 LSD. The car is noticeably slower, but I get better fuel mileage and it runs better on the highway. The power band is perfect for US driving conditions. 70MPH (120KPH) is maybe only 3500rpm in 5th gear, right smack in the middle of the power band.
School buses are faster from a dead start though...