They seem to work almost identical, catch wise. I do not have recorded if one seems to be better or not, but I have a feeling/hunch that I’ve trapped more hares with loop snares. Others’ experiences might vary.
For a nomadic; or seasonal traveler, I like loops snares (and paw-boards) for winter trapping grounds. Come spring time (no more winter skins), I go pick up the traps, leave them in barn/shed/cabin and head to summer location. I could go kick or even dismantle light lever traps, but I like to switch spots across winters. So the loop snares work better for that.
If you play stationary farmer who traps on the side, then light lever traps work great. Keep those birds from devouring ALL the sown seeds.