The 2 devices have a different signature. I added the 328 to my Arduino and AVRDude files so that makes it easier to burn a bootloader. Once the bootloader is loaded they are interchangeable in the Uno board so the Uno config is sufficient to program them. I have a couple 328's that I have installed the bootloader on. they have all been in my arduino board and also in a wireless breadboard that has a MAX232 for a serial interface. Once the bootloader is loaded they all function the same with the ArduinoIDE.
Functionally I think the only real difference is in low power operation.