with a LSD, if you only lock in one hub, the front will be useless. The open side will get all the power, and thus you will have no wheels turning in the front. If you had a locker it would be a different story. This applies to people with a rear LSD, if you have your rearend cocked up and one tire in the air, the tire in the air will turn, and the one with most traction will not.
A limited slip is just that...limited slip...it only sometimes limits slip. That is why I run lockers front/rear. You just have to be more conscious of your driving, and know how to drive. After a while you dont even notice it.