I have installed a torque-biased Quaife LSD in my previous 335 to smoothen out the torque delivery between the two rear wheels around corners. I was running in excess of 600 NM on the wheels and I had wheel spins on straights and slips around corners. I needed traction. The LSD took the torque and divides it between the 2 wheels and increases the bias ratio - a 2.5 : 1 ratio will multiply the torque that is going to the slipping wheel by 2.5 and transfer it to the wheel that has grip. Installation wise, gotta verify if the differential in your ride is bolted (pre-2007) or welded. Bolted version enjoys a direct swap against Quaife. Welded version gotta exchange the entire axle, if I am not wrong.
Your e-diff is still a differential lock (plus a computerised LSD), using chassis sensors such as speed sensors, ABS sensors and microcomputers to electronically monitor wheel slip and vehicle motion. When a wheel slips, the computer applies the brakes to that wheel instead of sending more torque to the slower wheel like the mechanical LSD.
So what's the difference?
The feel, especially if you abuse your car.
Both targets traction. But the positive driving feedback, confidence and control are different. The e-diff has it's limits. Once traction loss is too great, you will face a sudden loss in traction than what a mechanical LSD - you might spin more suddenly than with a mechanical LSD. This is mostly evident exiting corners under heavy throttle. This is where the mechanical LSD shines. Because the e-diff uses brakes to aid traction, excessive heat and wear may be generated on your rear brakes during track driving.
When would you feel the differences? Normal street driving? No. Spirited driving? No. Track and drifting? Yes, but only if you do.