@timbray
I guessed "no difference", mostly because if the answer were the obvious one (wired faster), you wouldn't have had the poll.
The detail that your bottleneck for both is your ISP makes this result fairly obvious. I suspect for local networking (to a file or media server), even your old cat5 can push 1Gbps, and your modern wifi between 200 and 800 Mbps (depending on location and random factors. I usually blame sunspots.).