Quads are better when you're dealing with hi-res models. Quads make better results when smoothed or converted to SubDs. Triangles are to be avoided as much as possible for this reason when making hi-res projects.

In games, though, you DON'T smooth or convert to SubD, and game engines automatically triangulate models. However, it's usually a good idea to triangulate the model yourself in order to make sure the edge flow is as you want it.