Both are good, it's just the two actions are slightly different.
拍is to touch something repeatedly. For example,拍a basketball, insteading of holding it.
抚摸or摸means to move your hand gently over something. Your hand never leaves the thing or person you're touching.
In conclusion 拍：It's like when the dog gets back the branch you throwed away, you would 拍(拍) him as an encourgament.
摸摸、抚摸:It's like you're giving the dog a massage.
Anyway, in most cases, I personally would say摸or摸摸, very casual. 抚摸 here feels unnessarily serious and literary.