One of my students was told by some salesman that she could use a 'universal bobbin' that would work in any machine. Needless to say, that was untrue. She was having all kinds of trouble trying to make a stitch, and as soon as I saw the bobbin in the bobbin case, I could see that it was not high enough. I switched out her bobbin, and it was fine.
Not all bobbins are created equal. Many look very much alike, but are not.
Most classic machines these days take ONE of the following: class 15, 15J, class 66. Class 15 and 66 are available in both plastic and metal. I don't think I have seen any 15J in metal. Singer 221, 222 & 301 all take a class 221 bobbin, and I have only seen these in metal.(There are other bobbin types besides these.)
The rule of thumb is, if your bobbin case/carrier has any plastic in its construction, use plastic bobbins. If it is all metal, you could use either. That said, I have found that some machines perform better with one or the other. If your manual recommends one over the other, I'd stick with that.