The only difference between towing with a LSD or Open Differential is gas mileage. An Limited Slip Diff. will eat up more gas.
The Facts: A limited slip will basically "limit" the slipping of the tires. When the vehicle is in somewhat of a straight line, the LSD will act as a locker (which keeps the rear tires locked together all the time), which in turn takes more engine to turn over the two tires instead of just one. The whole reasoning behind the Open Differential is for gas mileage/fuel economy. The LSD has clutch packs on both sides of the carrier, which inturn allows the tires to turn at different speeds in corners/turning. If you did not have the clutches, or the clutches go bad, you will either get noise or you would have a "wheel hop" type situation. For strict offroad, a locker is better than a limited slip. The limited slip is good, though, cause if you get one wheel off the ground (or on ice,snow,etc. -- anything where one wheel doesn't have 100% traction), the limited slip will keep the other tire that has better traction turning and allow you to get free.
Open Differentials are pretty much worthless, in my opinion. I hope this helps you out some.
-Drew