If it was a rabbit, the stems will be neatly sliced off at an angle. If it was a deer, there will be ragged tears out of the leaves or entire plants eaten to the ground. You could try placing a board near the plants and dusting it with flour to check for footprints. Slugs and caterpillars will leave holes in the leaves. If you suspect nighttime feeding by insects, wait until dark sets in, and go out and check plants with a flashlight; insect feeding would have commenced by then.
For identifying mammal and bird damage, this Web site should help: Wildlife Damage Inspection Decision Tree.
