We have a lot of wood pigeons round here. They shred young cabbage, etc. plants and rip up other seedlings. The only reliable way of preventing this we've found is to put netting over vulnerable plants. We have a couple of cages (which also keep the cabbage white butterflies off) we can use as well as a couple of cloches.
There are rabbits in the field but they don't seem to come down towards the house where our veg plot is. I guess our cats and our own activity in the garden persuades them they are better of staying away from our patch?
If you wanted to try to keep cats away too, I suppose you could look at electronic deterrents but I'm not sure how effective they are. My only experience is with a couple of rat deterrents I put in the roof. These did appear to work at first but after about a fortnight, the rats were back and we went back to getting the rat man in to put poison up there.