Yes, the bobbins and bobbin cases should be interchangeable in your 301s. In fact, that would be the easiest way to check your new machine ---take a bobbin case and bobbin from one you know works and put it in the new machine. Then you can take the new bobbin case and try it in a machine you know works. If the bobbin case still has problems, it's the case.
The newly manufactured bobbins and bobbin cases are notorious in that they often don't work well. What you want to try to find is an original or one that has been tested. The only place I'm aware of currently that has a supply of tested bobbin cases is Cindy Peters of "Stitches in Time."
https://www.facebook.com/pages/Stitc...73087319370566 I haven't personally obtained any from her, but she's active in another group where I'm a member and seems to have many satisfied customers.
Good luck.