It's not necessarily a given that Melee would have more. It'll depend heavily on character, match, and playstyle (like Ansou said). A Melee Jigglypuff probably doesn't input as much as a Smash 4 Sheik, for instance.
Either way, it's such a variable thing that to have statistical relevance you'd need to come up with an actual way to measure it, and then do so across numerous players at whichever skill levels you find relevant.
If you count directions as an input (which you probably should), it's probably fair to guess that both probably average two inputs per second when idle, and 4-6 in a fight. Also important to note that not all inputs result in actions, due to moves not being instantaneous and lasting multiple frames.