In a nutshell the ribbon that you choose depends on the environment that your label will be subject to and the label material you want to print onto. E.g. if you are printing an address onto a paper label you would need a wax ribbon.

The difference between branded and compatible ribbons can be compared to the same instance as branded vs compatible toner. You know that you can always trust the branded ribbon to produce a good print on your labels. However if you pick the right compatible you can easily get as good a print as you can with branded.