Hello everyone!

I've asked a couple "experts" about this issue and I don't even know if they had any clue, but I'm pretty sure it's straightforward for anyone clued up....

1. Had a Google Sites (old) hosted website and bought a new domain for it that was in use for several years
2. Finally switched hosting from Google Sites, but kept both the old website with the GS domain, and the new one on the new host but with the originally bought domain; most content the same on both sites
3. Organic traffic suffered a few months into the switch to the new host...

My dilemma: do I take down the Google Site website with the GS domain? Is it "competing" with the new site? Of course chronologically the old site content was added first, but the domain it pointed to had always been the same.

What might be going on?

Thanks for any help!