Neither. I do not hoard, I collect and I do not waste, but I do strip those old bobbins. In most cases the machines I get have been stored in a garage or a shed and the old thread just holds moisture to the bobbin. I strip them down and check for rust.
On the ones that are repaired and working I will leave whatever I wind to the bobbin because I've checked for rust and the machine is now indoors. Then I have no problem using a bobbin with thread on it because I know it's relatively fresh.