I very much doubt rats. They go for the real calories, like avocados, tomatoes, not the leaves. Now rabbits love leaves. Easy to fix, get your plants up where bunnies can't reach. Sit your plants if in pots on top of other pots. If in the garden, encircle with chicken wire.
Rats will climb most certainly but I doubt it is for leaves unless your neighborhood is really really careful about food for rats and they are starving. It would be handy to see the damage and know more about food sources for both. How tall are these trees? Do you entertain giraffes for instance? Deer? Koalas? Bear? Rabbits can climb but not that high. Rats, definitely if there are more high caloric goodies as I am sure there are. Not leaves. What makes you think of rabbits or rats? Have you seen either? Tell us more about your environment to include your zone, locale.
These new pictures look like rabbits. For some reason I was thinking avocado trees. Easy enough to fix. Killing rabbits will never work, not even temporarily. Get a roll of chicken wire, very cheap and install so that you can bury some of it. I'd use dimensional lumber and make panels that look wonderful. I love the rabbits. Baby bunnies disappear quickly. But my green house is secure. I also feed my rabbits and have hay strewn around from feeding my horses. If they got desperate they could dig beneath I guess but that won't be happening. I also feed the deer and elk with a few bales of mouldy hay. I feed the dang neighborhood and feral cats so they don't kill all the baby bunnies. My greenhouse garden is quite safe. The cats keep the rats and mice and bunnies in control. Harmony in the woods so to speak.