Go with both. Even wooden mouse and rat traps will catch birds and small animals. Snares are only good for one use. The locks can be salvaged. I would go with a big spool of different stranded wire. Also needed to make snares are a good set of cable cutters, 6-32 steel nuts, and a hammer or vise to close the nuts on the snare.I had forgotten about trapping, it was popular with some teachers and fellow students when I was in highschool 35 years ago. When I think about it all of the local land that was trapped on is now strip plazas and subdivisions.
Somewhere I read it is a good idea to have 12 snares or traps for each person in your survival group.
In the SHTF, no more bounty. But just knowing how to trap, shoot, catch them is worth it. Nutria have a fair amount of good tasting meat if butchered the right way. Their hides and fur are a resource in a survival situation.in Louisianna it looks like you can make a pretty good penny trapping (or just killing) Nutria, since the practice died out (pelts went from $5 to $1) the vermin are out of control, so now there is a 20-year (supposed) fund that pays $4 bounty per Nutria tail, which means that you can still sell the pelt AND either eat the meat or sell it to a restaurant (idk the inspection &/or health code laws for that tho) many of the finest restaurants have nutria on the menu.
seems a hell of a lot safer/more reliable than gator hunting