I went to Nancy's and thought it was terrible. Not good like Chicago deep dish. Shorty's Pub serves a really great pizza, two locations one on North Druid Hills and the other near Tucker on Lawrenceville Hwy. It is thin crust. Fritti is very good also, as atlantanative said.
The only deep dish i know of is Nancy's - I've only had it once and it was good, but not cooked through enough for me - maybe a fluke. For thin crust, I love Fritti - it's not inexpensive street vendor pizza, but it's thin crust and it's good.