What you've described as a '1 way' is something along the lines of a Detroit Locker, used in lots of oval cars and other more simple circuit racing cars, including V8 Supercars, not really a desirable alternative to a LSD unless you need to put a huge amount of power down with rubbish tyres.
The '2 ways' sounds like a fully locked differential, useful for drag racing and the odd circuit application like some Group C cars where a lot of power has to be put down in a car that is easy to drive, expect understeer everywhere and increased risk of breaking driveshafts.
For a normal track car a limited slip diff (partial lock power and coast) is normally the better option.