i have swapped the appropriate (abs or non abs) normal automatic 3.73 rear axle into an m47 car and its noticeably faster on the lower end without causing the rpm's to jump too high at highway speeds.

The E80 isn't quite a normal LSD, it has some interesting centrifugal features which make it a bit more 'on-off'.

First is that the clutch packs are set up very loose, so they do nothing at all under normal use, unlike the varying amount of pre-load in a normal LSD. It engages with a little spinning flyweight device when the left and right rotation varies by at least 100 RPM. Open diff, open diff, *clunk*, 'locked' diff.

Secondly, there is a different centrifugal lockout mechanism on the housing that prevents the diff from engaging over a certain RPM (which is roughly 25 mph). It's intended just to be a 'get going from a stop' type of traction aid, once you're rolling along it will spin one tire like an open diff.

I swapped one into my '93 wagon 5 years ago (+/-) and it does help with low speed traction. But it's still not a super stiff LSD, once engaged. It does transfer a modest amount of torque to both wheels, but it's not like both wheels will always reliably break traction together. It just makes it a bit more even if both wheels are on level clean pavement (vs. that passenger rear always spinning).

It's possible that my clutch packs are worn, though. Once engaged, it's pretty much like a high-preload LSD, squeezing stacks of metal discs together. Once they get worn (more of a factor on how it was driven vs. how many miles it had) then it won't work as well when engaged.

And some people trim off that 25 mph flyweight when installing it, so it will engage at any speed. This is primarily for higher HP applications where traction is an issue in 2nd and 3rd gears as well as 1st.
--
'63 PV544 rat rod, '93 Classic #1141 245 (now w/16V turbo)

Matt, It depends on your definition of "is it worth it?" If you mean--will the limited slip be worth the effort to accomplish your desire for better snow traction? -- the answer to that is -- yes it will accomplish the task--only you can answer the second part--is it worth the effort to YOU.
The other part to the equation is -- which ratio to use. Going from the 3.31 to the 4.10 is a big step. Your car will definitely have a lot more zip in the lower gears -- with the cost of flexibility in traffic with the shorter speed range of each gear (approx. 25 percent difference in rpm/speed with my "off the top of my head" math) and the higher rpm at cruising speed. An advantage may be the simplified installation of the 4.10 guts into the 240 carrier.
If you keep the 3.31 gears and add the limited slip to it you'll have the advantage of the LS but not gain any performance.
Here's my more complicated suggestion (but may work better) -- find another rear--one from an auto (AW70/71) 240 (I believe the 4.10 must have come from a 16v car) that will have 3.73 gears - big enough difference to be easily felt without going to near drag racing 4.10. Add the LS to the 3.73 rear and bolt it into your 240. Now take your 3.31 and sell it to someone looking for maximum MPG -- or to someone building a V8 conversion.
Whichever way you go--remember--the open diff and LS are bolted to the ring gear with LEFT HAND THREAD BOLTS (replace them with NEW -- available at any speed shop). -- Dave