Hi,
If you have a setup where dev is pushed to live, then I always recommend activating on the one which is pushed to the other one. If Dev -> Live, then on Dev. License activation is not required for the plugin to work, it only allows automatic updates, nothing else. If you regularly push one site to the other one, then updating on the origin should be sufficient.
If you want to update on both at the same time without pushing, then you can still do via manual updates.