Synthetic stucco systems typically do not have a drainage plane and therefore are a disaster. I love brick. I also hate brick. Let me tell you when I hate it. I hate it when it does not have a drainage plane behind it that is also an exterior vapor barrier.
Wet brick exposed to the sun is like a moisture capacitor which discharges to the cold side.
The cold side is the interior air conditioned space. I love brick when there is a vapor barrier acting as a drainage plane between the brick and the rest of the wall assembly. Most brick in the South is installed without functioning drainage planes and effective vapor barriers. If you are not going to use it right don't use it. They can't handle part load conditions.