The Black Dog has a hump in the upper mids, which makes it richer, but maybe also a bit "looser" than a Mule, which is supposed to have a more balanced EQ.
If you're after rock mainly, you could like the BD more, if versatility is key, maybe a Mule.
Combinations I would recommend:
Mule calibrated set
Mule bridge with Missisippi Queen or Stormy Monday neck
Black Dog calibrated set
BlackDog bridge with MQ, SM or Mule neck
Is your guitar acoustically rather bright?