I think this is a complicated subject without a single answer for the most part.
I think the Eaton clutch type is probably better on the strip by a slight margin and the TruTrac is better for all around driving and particularly on the street.
I had an Auburn of the original type and it was very notchy feeling going around corners on the street. It wore out in a few years and was putting power to only one tire-just like an open rear end. This was not the Pro version that came a bit later. If I recall correctly, the Pro was initially said to be rebuildable if you sent it back to them and paid a fee. Now it seems to be guaranteed for a year and then they will rebuild it for a fee for three more years...or something like that.
I replaced the Auburn with an Eaton clutch type with stronger springs, and it is not obvious going around corners like the Auburn so I much prefer it.
Today, I would probably take a long look at the TruTrac because 99% would be on the street and most reports say it is great for that and works well in the straight line launches as well.
I have not seen one of the modern Detroit Lockers so I cannot comment on them, but I remember the old ones