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No direct experience, but as I understand it: the Torsen is better for a road track car because it is a little "freer" in the corners and can take more cornering under power. The regular traction lock diff is better for maintaining traction in a straight line and I think it transfers torque better / more evenly across the two wheels.

Maybe someone else can chime in with a better explanation but I think that is fairly close.

Why are you interested, what are you doing with the car and what shortcoming are you seeing now or what improvement are you looking for?
 
Thanks BlackBarchetta and CDN5.0 for the helpful insights on the workings of these differentials.

. . . . I think I have a 3.31 rear end (according to a VIN look up I used when I first bought the car) and the MT-82. I'm also running a ProCharger P-1SC-1 (575 rwhp on a DynoJet). . . . . I mainly enjoy street driving the car, club "mountain cruises" at places like The Tail of the Dragon, and an occasion track day. Would my car benefit from a rear end upgrade? Should I consider a rear end upgrade or would my money be better served upgrading the brakes (non-Brembo right now), transmission cooler, and oil cooler? . . . I'm overly aggressive with the go-pedal, do both of my wheels spin or just one? . . .
I would leave the rear end ratio alone because I think you will have plenty of torque from that setup and I don't know why you would want a lower first gear. The transmission ratios are fairly close in the MT-82 so I think you should be able to find a gear that matches the situation pretty much all the time.

For the road track days it sounds like the Torsen differential might be a benefit in the corners. I wonder if the standard trac-loc contributes a little to unpredictable behavior in corners when near the limit. I am starting to think that I might want a Torsen myself; even though I cannot point to any definite instances where I have had a problem with the trac-loc . . . I am a fairly novice track driver so I can't really tell the difference on some of these fine points.

In your situation I think I would do the brakes first. The SVT GT500 Brembo kit is the "best buy" in my opinion, though you might be able to save some money by piecing together the parts rather than buying the complete kit. There are some threads on here with the details about that.
https://www.americanmuscle.com/svt-brakekit-0509gt.html

I had an issue with my rear brakes getting really hot during road track sessions and cured it by installing the larger GT500 rotors with adapter brackets from the guy on e-bay . . . very cost effective and easy upgrade.

Then I would at cooling if you are having any overheating issues. I have heard from several guys driving the 13-14 GT's on the road track that they do have issues with the oil getting too hot. Also have heard that the Boss oil cooler is not the best solution.

The purpose of the "limited slip" differential is to make sure that both wheels spin, not just one -- so you should be getting two-wheel burnouts, not one wheel.
 
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Cool video!

but, even though I am a mechanical engineer, I still don't really get how it works to allow the car to go around corners . . . does the outside wheel basically free-wheel; with all power transmitted to the inside wheel?

I guess I need to watch it again, LOL
 
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