My friend and her husband are both vegan, so I'm sure any animals they keep, they will not be wanting for meat. They have been thinking about chickens or ducks for eating slugs and weeds and food scraps. Will bunnies or chickens eat English Ivy? I know my chickens and ducks do not eat blackberry vine, and the chickens don't seem very interested in eating bindweed. My ducks never did too much to the bindweed, either. Right now, I have my chickens' run where my bindweed grows and there's blackberry that's grown in there, too. They haven't touched the blackberry, and have slowed the progress of the bindweed...but I think a lot of that slowing is caused simply from me going down there more often and pulling the weeds.
My chickens are not interested in most woody or hardy plants. Overall, I find they are a bit picky preferring the soft herbaceous plants. My chickens won't really eat mature grass even. When I only used chickens on a piece of land, all of the woody weedy plants and vines would take over because the chickens ate or scratched all the competition. Chickens and ducks are really omnivores preferring bugs and worms.
Rabbits, on the other hand, are herbivores. Mine are not picky at all. I have not seen anything they won't eat but I have not given them English Ivy. I even noticed that they will sparingly eat things that are supposed to be poisonous to them, but they will eventually eat it. They will definitely eat Japanese Honeysuckle which is a big pest around here. They don't prefer it but will nibble it and take it on back if left on the honeysuckle patch. They will definitely eat blackberry and greenbriar. Mine love the leaves and will even nibble green stems. They will strip saplings of bark so can be effective against shrubs as well. You can greatly increase their efficiency if you cut or even knock down tall weeds so they can get to them more easily. The biggest difficulty with rabbits is the difficulty of keeping them fenced in. It requires burying so you can't just put up a temporary fence as with chickens. Honestly though, if you are not harvesting the rabbits, then you can handle them often and they can become your buddies. They won't run away from you so it's not a big deal if they escape unless you have predators. They won't go far and you will usually find them next to the fence.
They will use the same watering nipples as chickens as well. So I rigged up a 50 gallon barrel that gravity feeds down to the rabbits and chickens and they can all drink from the same nipples. The barrel collects some water in rain but I have to fill it every now and then. I don't have very many right now but we used to have about 15 rabbits and 6 chickens being watered for almost a week with the 50 gallon barrel. It makes it very easy to take care of. In winter, I put a trough heater in the barrel, and I also ran a hose coming back from the pens to the barrel so I could hook up a little pump to keep water flowing through the lines in the winter. It works well into the 20s at least. If you buried pipes from the barrel to the pens, it would be much better. If you are collecting rain water for the barrel, do check the nipples now and then to be sure they are working as sediment can clog them. I just unscrew them and clean them and they are good for another several months to a year. Getting a bit off topic now so I'll stop.