Round bobbins come in metal and plastic, is there any difference apart from the looks? Yes, there is.
Metal bobbins should be heavier, and most of them are. There are some “fake” metal bobbins that are either plastic painted silver, or they are made of some alloy which is very light, I presume that’s aluminium. I don’t know how these alternatives behave, so I’m focusing on the standard metal bobbins which are mostly steel.
Modern machines are quite happy with plastic bobbins, and if they also have a plastic bobbin surround, then even more so. Vintage machines are a different matter, even if they are of the same design. They absolutely dislike plastic bobbins, and as my old Jones manual puts it, “it leads to no end of trouble”. That was a warning about using any other oil than sperm oil, by the way… But never mind that. 🙂
Sewing machines are actually high precision machinery, with tolerances often under 0.5mm for parts and needles – get the size wrong by more than that, and it won’t stitch. The bobbin is an interesting part because it goes from full to empty, yet manages to maintain the same thread tension through the bobbin case or holder. The thread is clamped under a spring which generates that tension. But the bobbin also rotates and rubs against the walls of the case or surround, which adds to the tension. The bobbin rotates because your sewing pulls on the thread, so thinking about it, a full bobbin should be harder to move than an empty one, and the tension should be gradually decreasing as you’re using up the thread. Which would be a disaster.
In fact, this is exactly what happens with plastic bobbins in vintage machines. They start out just fine, all the thread makes them heavy enough to work properly. But towards the end, they become too light and start jerking and jumping on the surface imperfections when their sides rub against the walls. This leads to pulled up stitches because the machine fails to pull them tight which is done with the bobbin thread.
Sometimes it also produces stitches with visibly different tension.
Similar things can also happen with metal bobbins if the bobbins or the bobbin case is dirty, rusty or scratched. But it can be fixed by cleaning and polishing it all until it is nice and smooth. Wipe it with a tissue soaked in oil, and you’ll have a lovely thin oil film coating that helps gliding but does not oil the thread. Note that it can make things worse for plastic bobbins because electromagnetic forces between the molecules in the plastic and in the oil film will try to bind them together instead of letting them glide…
Stick to metal bobbins for vintage machines, if possible. Plastic bobbins will also work when they are not quite empty, so the solution there would be to have some thread on them as a “buffer” just to make them heavier. Experiment with your machine to see how much that should be. Then you wind your actual sewing thread on top of that. Make sure though that the two do not get entangled!