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the supra auto 3.76 lsd that's the WHOLE unit (the whole pumpkin), so it's a direct sway. it's a torsen type lsd.
the trd 1.5 is just the lsd unit, you need a GOOD shop to take out your stock rear end, open it up, and install the lsd. it has to be done carefully otherwise you can mess things up. trd lsd is disc type
you can google to see the difference between torsen and disc type lsd, and see what's the pros and cons
to me, i went with the supra 3.76 lsd. it's more expensive, but the swap is easy and cheap. later on when i sell the car i can easily swap it back and sell the lsd unit. plus, i care more about the 3.76 gearing more than the lsd anyway. honestly, unless you drive the car really hard (and i mean REALLY hard), you probably won't benefit that much from the lsd