This is probably a dumb question. I know that the LSD transmission is better just because I have heard it from so many people. But what are the real advantages of having an LSD tranny. Is it worth an extra $300 when buying a swap?

yes it is worht the extra $300. the whole point of a lsd equiped tranny is unlike the open differential tranny which only spins one wheel the lsd tranny locks both wheels to keep them both spinning. this improves handling and acceleration.