For many pieces I just toss my pieces in the tumbler, especially if I'm going to dip them in Liver of Sulfur. But the tumbler treats each piece equally and they all come out of the tumbler with the same overall shine.
The benefit of hand burnishing (shining) the metal is that the artist can be selective as to what gets burnished. My latest pair of earrings (which I made during the play day at Carol's studio) definitely cried out to be hand burnished.
Carol had a couple of texture plates that looked like weaving (which I don't have..... that's why I tried them.) Being a past weaver (well actually not all that long ago) I know that different textures and colors add to the weaving. Hand burnishing gave me the opportunity to create the difference between a "satin weft" (the threads we weave with) and a "shiny warp" (the threads we weave on.) These earrings are simple, but I like them. Now I have myself a new pair of earrings.
I've got some other ideas to incorporate weaving techniques into my metal clay. Just got to find the time to do them.