I started researching this on the net and it seems that there are a ton of contradictory opinions out there. Here is what I have found so far:

As a general rule, if the bobbin case is metal then use metal bobbins.

As a general rule, if a machine is sold with plastic bobbins then use only plastic bobbins in it.

Older vintage machines came with metal bobbins, but plastic bobbins work in them. The only thing is that switching between the two can cause changes in tension.

Metal bobbins of the same class can be of different qualities. Vintage metal bobbins were machined accurately, but some of the modern metal bobbins are not machined as well and can cause problems in some machines.

Finally, I found this which seems to actually directly address the original question:
"10 pack of plastic class 15 bobbins fit all class 15 drop-in rotary or oscillating hook machines, whether older front load or newer top drop in class 15 bobbins. It is ok to use plastic bobbins in metal and plastic bobbin cases. Metal class 15 bobbins should only be used in front load metal bobbin cases as it may cause undue wear on top load plastic bobbin cases, but will work fine."

We had a fairly new sewer in our guild and she was having all sorts of problems with her machine. When I went to help her I noticed she had both metal and plastic bobbins and I asked her which came with her machine. When she put in the bobbin that came with the machine she didn't have any problems at all.

I would say if you want to spend time fighting with your machine use what ever you want. If you actually want to sew without problems use what came with your machine.

NO NO NO NO NO...In some machine a metal bobbin will ruin the bobbin case and then you will be up a creek.....
Please don't chance it....

I have a drop bobbin in my Janome Gem. I use metal, plastic, and the paper sided bobbins makes no difference in the sewing and it's over 5 years old and no problem. The plastic bobbins can be mishapped sometimes right out of the package so be careful about buying them too cheap.

I have a Brother that takes class 15 bobbins and I use either metal or plastic. I get the same good results with either one.

If I'm not mistaken the plastic bobbins came about when they started making the low bobbin indicators on sewing machines. The mechanics of it was that the low bobbin indicator could not read through a metal bobbin to let the user know of a low bobbin. That is what I was told by Pfaff. There are any number of higher speed machines that do fine with the plastic bobbins. They are engineered that way and are not really made of what we think is plastic...it is another type of high grade material that has no problems with high speed. I think there is a lot of misinformation out there about bobbins.

That said, if your manual says use only XYZ bobbin then of course use only that type of bobbin but a I don't think a plastic type vs metal type class 15 will make that much of a difference. Both types can warp with a lot of use. Also some newer machines aren't made with the all metal bobbin cases and the metal bobbin may be too hard on them. I am speaking of the less expensive machines that are available today. However the higher end machines should not have a problem with either unless you have a low bobbin indicator and want it to work properly...then you need to use a plastic type bobbin for your specific machine. Again, these bobbins are NOT plastic but some new high grade type material that were created specifically for these machines.

That's because the bobbin doesn't spin in a drop in bobbin machine.

To a guy, reading the manual is the same as asking for directions....

I bought my first Brother last summer. I asked if I could use my metal bobbins and I was told if I used the metal ones they would chew out the bobbin case. It came with plastic bobbins for a reason. Don't use the metal ones if you want your bobbin case to last a long time.

I have an old Singer and it is all metal so using the metal ones in it is just fine. I also use the plastic ones in my Singer but doing the opposite of useing the metal in your Brother is not a good idea.

what I was told is, you can use plastic in place of metal but don't use metal in place of plastic. The metal bobbin in a case made for plastic will cause too much wear. don't know if this is true but it does make sense.