If you do them properly and you have your values correct, there should be no difference what so ever. If there is any significant difference, there was an error in measurement.
I completely agree that mixing by weight vs volume would be identical if you had all the necessary values for both methods. My proposed experiment would simply be mixing the same recipe using given percentages by weight and then by volume. This would not take into consideration that some ingredients would have different values between weight and volume. The reason I believe that there could be different outcomes is because when mixing by volume (for say a 30ml bottle) you will inherently end up with 30ml if you mix ingredients that have a total volume of 30ml. If however, you make a batch of juice using ingredient percentages by weight, I believe it would be unlikely that you'd have exactly 30ml of juice when the percentage of ingredients equaled 100%. I think what would happen is that once all flavor and nicotine base was weighed and mixed, you'd inherently have to complete the juice by adding VG/PG by VOLUME to end up w/precisely 30 ml of finished juice. I hope that makes sense. I'm not sure that I'm explaining my thoughts on this as clearly as I'd like. I do agree that the practical difference is probably minimal. I've got a couple of chemical engineer buddies that should easily be able to set me straight.
Charles