I think the best test is to place one wheel on a low traction surface and the other on a high traction surface - like dirt/asphalt, but ice/dry pavement would be best, then give it the boot. Be aware that normal street type limited slips can go into one wheel spin if the torque differential overcomes the clutch torque capacity, so don't get carried away.

Limited slip differentials are rated at "percent limited slip" which is the torque differential allowed before the diff begins to lock up. Street oriented verisons are usually no more than 30 percent, or they can be jerky/chatter in normal driving.

Duke