Norm,

For our method of freeze branding we had an insulated aluminum canister that would hold 1-2 gallons of liquid nitrogen. At the bottom of the canister, protruding from the side, was a large brass nipple. We would hold the fish firmly up to the brass for about 3 seconds. It would leave a fairly distinct mark. Sometimes we would do this after clipping the pelvic fins to slow or prevent regrowth. It was described to me as leaving a scar. It's cold enough to disfigure and permanently damage the skin cells. However, as a long term marking tool it didn't work well for us. It was the mark that was the least distinguishable after a couple of years. We didn't do any studies on tag retention, but I'd be something could be found online. From my experiences, in general, a good pelvic clip close to the body will give you atleast 2-3 good years. Hopefully you could catch and reclip the fish as they grow. You could clip one pelvic fin and leave the other as a reference if one does regrow. Sometimes one can notice subtle differences in the fins that have regrown.
FYI another marking technique I've seen for multiple groups of fish is removing one of the several dorsal spines. Depending on which spine or spines were removed indicated to us which group of fish we were dealing with.
I typed in "freeze branding fish" in google and found several articles on the subject if you want to learn more.

Mike