grip tape has a better feel by far IMO. when im riding a foam topped board, it feels like my feet sink into the foam a bit and it makes it a bit harder to shuffle my feet around on the board. i also like the solid feel grip tape gives. foam cushions your feet a tiny bit, but grip doesnt do that so it makes me feel more "attached" to it.
grip will burn a bit if you fall on it wrong, but ive never had a problem with it damaging the boat in any way. just be careful like you would anything else (boards with fins, carbon handles, etc).
oh, and you would fall on your board if you try shove its, kick flips, and wake to wake stuff. if you are just gonna cruise around and maybe practice riding switch or something you probably wont ever fall on your board.