Hi Dana,

How much of a difference is there between the two ceilings? I'm curious why they are off. If they are not structural issues to factor in, then the faux beam would be a nice way to hide the transition. The beam height and width should fit proportionally in the room, so ceiling height is a factor. You could also add additional faux beams in the room with the lower ceiling, if that would work with your overall design goals.
-Steve

Place a wood timber beam of at least 6 x 6 but don't paint it white - sandblast it first so it looks reclaimed and like it has been there forever.

You could also, sheetrock around beams, paint and add crown.