I have only stayed at the Andaz once but was eventually upgraded to a suite there. They must have some good suites, but the one I got was pretty strangely laid out -- two rooms around a corner connected by a door through a short diagonal wall.
Based on that experience, I'd pick the Churchill in a flash, where I've always enjoyed the suites.
Better yet, change your plans to go to Paris and stay at the PH Vendome!