I agree with the consensus on this thread and say this is a very odd comparison because you couldn't compare two more different cities. There is enough information on these boards about Atlanta, so I'll enlighten people about Savannah.
It's not a major or big city. It is however an
importortant city due to it's history, culture, and architecture. In modern times it is important because of it's tourism and it's port (which I believe is the second largest on the East Coast). Because of this, Savannah has a small town vibe among it's people and it's "pace". You get the sense, especially in the Historic District, that the residents all know each other.
The culture of the area is primarily split among the descendants of the Colonials, Irish and the Gullah. "Voodoo" (I don't think the Gullah call it this) is commonly practiced in the area, and oddly enough, Savannah has one the largest St. Patrick's Day celebrations in the country. In other words, mirror mini New Orleans (British settlers instead of French, Gullah instead of Creole, and Irish instead of Italians).
It is also a very old city, which is not lost on you as you walk the streets. How old you ask, Savannah was planned and incorporated in 1733. It's of about the same age group as Baltimore, Philadelphia, Charleston, New Orleans, Providence, Boston, NYC. The planners designed it specifically to be Georgia's major city in the same vein as the one's above.
Even though Savannah survived the Civil War without any major damage (The residents boozed up General Sherman so he wouldn't burn the place down like he had Atlanta), the war undoubtled had a major effect on the city. As many people know, the South was utterly destroyed after the Civil War both politically and monetarily for almost two generations. In the years after, it was anyone's game to become the dominant player. However, Savannah did not take advantage of this and focused on it's shipping ports instead of rail. Atlanta did, and became Georgia's (and the Southeast's) major city.
This is also the point where the huge differences between the cities becomes apparent aside from the obvious one that the area that is now Atlanta remained a Creek and Cherokee trading town for 100 years after Savannah started building it's famous squares.
Cuisine: Savannah has by far the best Lowcountry cuisine in the world. While the restaurant scene has been growing over the last few years, other cusines leave a lot to be desired since they do not have a large pool of talent pull from. Case in point, the worst steak I have ever had was in Savannah. What they did to that meat should be illegal.
Arts: Also because it is a smaller city, you won't find a lot of art tours, bands, etc there. The local scene is pretty good.
Entertainment: This where Savannah shines and fails. On the plus side, you can consume any beverage on the street as long as it is in a plastic cup, the residents are fun loving, and clubs stay open until the wee hours of the morning with a nice variety of music from blues to punk. But because of it's size, you are likely to hear music in the clubs that is as much as 6 months or year behind clubs in Atlanta. There are no posh night spots, and the clientele is more of the college frat type. While it can still be fun, it's not my cup of tea.
Diversity: While the culture of Savannah is unique, it is not particularly diverse. For those who think Atlanta is "just a black and white city" have obviously never been Savannah. While this is not a bad thing per se, it is a big reason why Savannah is not at all cosmopolitan.
Business: While there are several options for work, the city pretty much revolves around tourism. Something that is not at all friendly for upwardly mobile young professionals.
Overall though, Savannah is one of my favorite places in America and enjoy every visit I have there. Everyone should at least make an attempt to check it out once in their life.