I have both, but only female bettas. I don't like the ugly (IMO) frilly fins on the male bettas. Goldfish come in several colours: orange, yellow, red, brown, bronze, silver, blue, white, pink, bi-colour, tricolour, calico, tortoiseshell. Of course bettas win with colour since they can be any colour or combo in the rainbow and then some. Goldfish have 30+ breeds and varieties. I own a wild type, commons, comets, fantails, oranda, and jikin currently.
Here's some varieties. If I had a Japanese-type tank I'd die to have tosakins.
http://www.elgoldfish.com/variedades.html