I've SCCA road raced (wheel to wheel) I suppose four types of devices in rear wheel drive cars (260Z and Miata): a welded diff (essentially how your locker will behave on the track), a clutch pack LSD, a Quaife (ATB, Torsen) LSD, and a viscous coupled LSD. I have a differential with one of each except for the viscous coupled LSD.
Of these my favorite is a properly adjusted clutch pack. It has great traction under power, turns correctly on decel, and is robust. Adjustable, works well, and you'll find most folks using these on the race grids.
The welded I grew to like but it has a few things that must be dealt with. First, as you've noticed, it will push the car. You can adjust your suspension and driving to take care of that. If you do you'll find it has fantastic traction and power application. Better IMHO than the clutch pack. But, there are drawbacks. It saps power in turns since it is always causing one tire to slip since there is no differential. On/off power transistions can cause the car to slightly change directions. And they are hell in the rain. Plus a complete bitch to push around in the paddock. However, I like the welded on big long tracks without a lot of turning, when it is dry.
The Quaife ATB (Torsen, goes under other names) works pretty well and I think a lot of guys start off with these when they begin to race. They require no maintenance, work reasonably well as far as putting power down. But they have draw backs in situations where one wheel is unloaded heavily or not in contact with the pavement - they don't work. You can adjust your suspension to minimize this but you might not like the results. You don't find many of these in use on the pointy end of the grid.
Viscous coupled LSD - this thing is basically only for street cars and to help a tiny bit in snow and rain. On the race track they get hot quickly and stop working. Not that they worked much in the first place. Not recommended for track work.