Beav, you ever see fox trappers that followed Oberto's theory of no pan? And guide to hit the shank or cut down pan? I have some old traps modded that way and they work just fine, if you have foxes.

There are uses for all the size traps or they never would have been made. One size never fits all and one style never fits all; unless baggy,tight and ugly are what you like.
On land I'll probably never use bigger than SVS#4 nor smaller than Vic1 1/2 in coils & #2 or #3 LS although have bigger and smaller and have used them.
I like the LS traps, but can carry more coils in one pocket given the same size; so if trapping right under the truck or with a pack mule would likely chose LS, but when hiking would use coils.
Same thought goes to bedding and covering, soil type and condition might determine what I grab.

How large is the targets foot? Coyote and cats make the biggest track in my woods and I have never seen one that would not fit in a 1 1/2 coil.

How do they get damaged? IMO, damage is in how they fight the trap after the catch is made and how the trap fights back and this might be determined more by the chain length, anchor system and available cover than by the trap, although a heavy LS might tire them quicker than a coil.

Type of set might favor big over small as could snow. That #5LS wouldn't be much fun in a step down as might be used around stock.

I let the circumstances chose the trap.