As we know Apple is deprecating developers' access to UDID. But to my knowledge it is possible to get an iDevice's MAC address. So what's the difference then? Both MAC address and UDID are unique identifier of a hardware, which is not app specific.
Some obvious differences between UDID's and MAC addresses:
It's conceivable that a device might have more than one MAC address.
Guaranteeing uniqueness for MAC addresses isn't Apple's responsibility.
UDID's and MAC differ in size and format.
I think it's best to consider the deprecation of the UDID as Apple's way of encouraging developers to switch to other means of identification. For example, keep track of the user rather than the device by setting up a userid/password system. Tracking the UDID brings some problems, like what to do if the user loses or sells his or her device.