I went to both on my (first) honeymoon, which was in 1995. I preferred Savannah. It was a good deal quieter and far more relaxing than Charleston.
I did think the architecture in Charleston was amazing. Still, it felt like a louder, bigger city, even when comparing historic districts. I think both are about the same size, but historic Savannah felt like a trip back through time. Historic Charleston felt like a trip through the Travel Channel.
Savannah is an awesome town. Lots to see and do around there with some great low country food. I think there are a couple of threads on it if you search Savannah on this forum.
Both are good cities to visit.
Charleston: a "clean" New Orleans; more and better restaurants than Savannah.
Savannah: good for a couple of days; grittier than Charleston; good history - take the horse-drawn carriage tour; stay in one of the old hotels with a room overlooking the river - very impressive to see a ship cruising right outside of your window; Paula Dean's is very good, but a hassle to get the 'reservations ticket".
Lived in Savannah for 4 years. It does have decent qualities. There are some outstanding restuarants on the squares. Cant't say which one, cause its been over ten years. The Riverfront is not too shabby.
I would however go to Hilton Head, given the choice. Savannah in Auust is brutally hot.