A wired connection will often be a little faster. But really it's more to do with stability, a wired connection is more stable because WiFi can suffer from interference, specially if your router is in another room from your PC/Laptop/PS3. But, if your device is a long way from your wired router, and you have to use a very long cable, your connection will be slower anyway.
I use WiFi, with 10Mb cable broadband, and a Netgear WiFi router, and I find that it's fast enough to stream movies, and play games online, on my PC and PS3, but, my router is in the same room as my PC and PS3.
So, if your router is close to your devices, then a wired connection will be more stable, and better for streaming, and specially for downloading as you won't get breaks in the connection to stop a download. But, if your router is more than 6-10 feet from your devices, then I'd recommend a WiFi connection if you have fast enough broadband:)