L/S does double the traction, since you now have 2 drive wheels instead of one, but its even better than double, if thats possible, lol
An OPEN differential is worst case in slippery conditions, because it sends all the power to the EASIEST to turn axle/wheel
So once one wheel starts to slip 100% of the power is transferred to that wheel................yes, worst case indeed
So if one wheel is off in say mud, on the side of a dry paved road and one wheel is on the dry paved road, the wheel thats slipping in the mud gets all the power, so you are stuck even on a dry paved road
Limited slip sends power to both axles/wheels all the time, if an axle/wheel starts to spin faster than the other, power is SLOWLY transferred AWAY from the slipping wheel and to the wheel with better traction
The "slip" part of "limited slip" comes into play on dry paved roads when going around a corner, the outside wheel needs to spin more because its on a longer curve that the inside wheel on the corner, so L/S allows that axle to "slip" so wheels can turn at a different speed if the difference is not that much
Locker is really for off road only, or very specific on road situations, and can be dicey even then, at speed
In slippery conditions where one wheel and then the other will switch from good to poor traction the locked wheels can send you sideways as one wheel suddenly gets good traction, and when cornering one wheel has to be dragged because both axle/wheels MUST turn at the same speed
Lockers do have their benefits, but also drawbacks, for street use a manual locker would be best, it would have an ON/OFF selector, so could be used at drivers discretion, this would be an OPEN axle when off and a Locked axle when on
In my opinion a limited slip is the best overall choice