Frames are generally made of two materials: wood or metal.
The metal of choice tends to be aluminum (or ‘aluminium’ if you’re in the UK or down under), while wood types vary widely.
When it comes down to deciding which is better, it’s pretty subjective as there is really only an aesthetic difference between the two. Metal frames allow you to have a thinner profile on a larger picture, while wood frames need a certain thickness to keep from bowing with larger works.
Although they now come in a variety of finishes and motifs, metal frames are still mostly used in the standard square or round profile in silver, gold or black. Wood mouldings have always been offered with more options, they even come in slick metallics that appear to be metal. And of course a metal will never look like natural wood.
As a framer, I much prefer putting wood frames together over metal so I tend to steer people in that direction. Also, design trends tend to sway to and fro on this issue - currently, wood frames are in the lead. I do think that a nice thin, brushed silver frame will always look good with black and white photography… but what is your preference?