A wired ethernet connection will always be more reliable than a wireless connection. In terms of speed, this is likely to be most significant in a Local Area Network where files are transferred between computers.

As far as the internet is concerned, unless you have a broadband connection of about 50Mbps, your connection from the computer to the router will always be much faster than your download internet connection, so wired or wireless makes little difference. Having said that, if you are running more than one computer "wirelessly", the available bandwidth is shared by them, unlike wired connections where each will have the full speed of the router's network switch, usually 100Mbps.