Both of them will appear in GC. If you use GC as your definitive record you will need to delete one or the other.
If you use Strava and you start the two at more or less the same time then the first one to get there will "win".
The "problem" with rotating your watches is that training load won't work properly as the watch needs to see all the stuff you do. So, if that matters to you, wear at least one of them all the time.