With sticky good tires, yes a LSD will help out. With tires that are easy to spin you probably wont notice a difference, as even an open diff can break both sides loose.

 

What are the signs of a worn out LSD?

 

From my experience driving with snow and in mud the limited slip helps a lot. IT not only gave the car more traction but made the car step out predictably and more controlled than with the open diff. In my opinion open diffs suck and should not be put on cars anymore.