I've stayed at both, and have to agree with what's posted above. The one thing I would add, as someone who's never been upgraded to a suite at The Olive, is that I've never had a room there with a bath; only large shower area. I've always, even if not upgraded to a suite, had both, not so large an area for the shower, at the GH. As I stated, never been in a suite at the Olive, so don't know if they have both there.
So, if taking a bath is something you or the SO might like to do, then look to the GH.