Both types of ADS-B use transponders. If you're using a UAT ADS-B transmitter (978 MHz), you're using that in conjunction with a Mode C transponder. (You're not just picking up the altitude from the transponder -- the transponder has to be present and working.) If you're using Mode S ADS-B (1090 MHz), you're uisng a Mode S transponder with ES to do that (it serves as both a transponder and an Extended Squitter, which sends the ADS-B data). So, regardless of flavor, you need to keep your transponder in working condition, which means it needs to get a checkout every 2 years.
ADS-B is not just about the new data that gets sent out (tail number, ICAO code, etc), it also still requires the transponder functionality.