I would check out (google around or check out photographer sites) for photos from past weddings done at both to get a better idea of all the different concepts hosted at both venues.
Personally, I'm biased as a CBI bride. I literally could not have asked for anything more than what CBI gave to us.
I've been to a wedding at Wychmere and it was absolutely beautiful! Never been to Chatham Bars Inn though so unfortunately I can't give a very fair comparison. Good luck
Re: Wychmere vs. Chatham Bars Inn?