The Janome and Bernina bobbins are the same in height and width. But the Bernina bobbin center hole is a little tighter. You can tell them apart by how many holes are in them. The Bernina ones have 7 holes, and the "class 15" bobbins have 10 holes. The 10-hole bobbin work in a lot of different machines. But as you've discovered, the Bernina ones will work in other machines, they just can't be wound on other brand bobbin winders.

I use the plastic bobbins as that is what came with both the Brother machines I have. To me if it came with metal ones or if there was something in the owner's manual then I would use them but since they didn't I stick with plastic.