Four Seasons is in Midtown. RC Buckhead is in Buckhead, of course.
All of Atlanta is arranged along Peachtree Street/Peachtree Road, so you have a long thin line of office and residential towers that stretches for miles along Peachtree, but when you get just a few blocks away from Peachtree, you can have single-family houses. (Think of Peachtree as somewhat like Wilshire Boulevard in LA.) Peachtree runs from downtown (old, gritty, not so nice anymore, except for the area around Centennial Olympic Park) through Midtown, then into Buckhead. FS is on 14th Street, a block from Peachtree. RC-Buckhead is at the corner of Peachtree and Lenox Road, at the same intersection as Lenox Mall and Phipps Plaza (two of the top-end malls in town).
Buckhead has long been considered the posh area of Atlanta, and 20 years ago Midtown was a fairly seedy place. Now, it's been pretty much totally cleaned up, save for a block or two here and there. Restaurants are scattered around town in all kinds of different neighborhoods, so you'll have to drive from either hotel. Both hotels are kind of surrounded by office towers and residential towers. The FS is actually in a hotel/office/condo tower, among the first of its kind in Atlanta. But the FS is closer to some of the few real walking neighborhoods of town, and in walking distance of the residential and commercial districts of Midtown, whereas RC-Buckhead is totally surrounded by malls and parking lots and offices. The High Museum of Art is walking distance from FS, as are Piedmont Park and the Atlanta Botanical Gardens.
The Dining Room at the Ritz has long been considered one of the top restaurants in town, and has spawned a string of chefs who went out on their own after leaving the Ritz. But I've heard that the Dining Room is closed now for a revamp, and I'm not sure when it will reopen. Park 75 at the FS is good, but not a super-high-end fine dining experience, if that's what you're looking for.
On balance, I'd take the FS. But that's easy for me to say. I live and work in Midtown. And I walk past the FS twice a day on the way to work.