WLAN itself can be protected by WEP-40 or WEP-128 encryption. Both are insecure' in the sense that it takes comparatively little effort to crack them.
But: Internet Banking is secured by SSL, if you log onto another computer using ssh, it's also encrypted (using a safe' algorithm), thus safe.
If you use the cable, you are not more secure, even less secure. It is just a bit more difficult to tap into your line. But that depends on the setup. If you plug your computer via regular ethernet, in a shared subnet, all your traffic may be recorded.
So: if you use ‘safe' services that offer extra encryption, WLAN is just as safe as the good old copper wires. If you are really paranoid about security, use a VPN in either case.