The Mk1 N/A MR2 uses a similar C series box, but with a different bell housing so it wouldn't be a straight swap, in no way, shape or form would it be an upgrade. The Mk1 S/C MR2 uses an E series box, again it has a different bell housing and would be a near impossible swap. The SW20 MR2 uses an S series box in the N/A and an E series box in the Turbo, both have a different bell housing and again would be a near impossible swap.
It's common to find an E series box with a LSD, but non of the above came standard with a LSD. Also the gear shift assembly on an MR2 box faces the front of the box rather than the back, so actually connecting the gear stick to the gearbox in a FWD set up would be a mission on it's own.