Liches are potentially the strongest. They have more resists and phylacteries give them a lot of extra abilities, a key thing is that their magic cannot be dispelled which is a problem for other undead as their lag protection can be.
Mummies get some abilities to give them an advantage in using their armies. Being able to hide them and also summon them all at once has some great uses. Some niche pieces of gear that work for liches do not work for mummies. While it is rarely used mummies can also become "alive" again. That lets them enter organia and eat.
Wights have more gear restrictions and less good vulns/resists. Their advantage is that becoming a wight has a 100% success rate.
Disruption is also a little weird. Lich can disrupt anyone, mummies can disrupt liches but not other pc mummies. Not sure what wights can do