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I like the idea of Automatic lockers such as a Detroit, so you don't have to remember to turn them off, on mine, it has blinking lights on the dash to let me know its on, therefore, it draws my attention to the dash and "Oh.. I need to turn that off when I get up there! " kicks in. but if it was a rocker switch on the dash, or toggle switch, I might overlook it being left on, until I tried to turn and couldn't.
Dennis had a Detroit front locker in his dodge, and it seemed that it didn't have any trouble turning sharp. Which reminds me, I need to get him up and going again with that old truck before he decides to sell it.
For that big of tires in the front I would use a Detroit Locker. It will unlock when you lift on the throttle and are in coast mode.
I don't like selectables. I cain't see well or hear well and I would use it enough that I would just ignore it and leave it in too much. And just more stuff to go wrong and cause trouble. And they are like a spool when locked in. Hard on steering stuff.
Torsen works on the different speed of the right vs left tire. With that large of a tire your axle revolutions are reduced. And the effectiveness of the unit is also. If you were running 28-31 tires it would be worth considering.
Lunch box lockers work like a Detroit but are not as strong. With that big a tire they would be right in there with lock outs for taking along extra parts. I always took my spider and side gears with me when I was running a lunch box and have never run larger than 33's.
Clutch type use friction plates to keep both tires going the same direction. Again the taller the tire the more leverage pushing against it.
Spool is just locked all the time. Course ya could just jump out and unlock a hub every time ya needed ta turn.
That is the basic stuff. And folks are different in what they do so there are exceptions.
I want to say that many people with 36-37 inch tires are running either Detroit or ARBs air or electric. Mostly because it takes so much force to turn a 36-37 inch tire, that the Lunchbox locker would always be engaged.