I would say Compassion (Indigo) is one of the most defining aspects of any Batman, so it'd work for either Terry or Bruce... but for Terry specifically, he has a love (I know, girly Violet) for what he does, and people he loves that drive him to keep being Batman, which is more unique to him.

But this is including the ending ep of JLU in my beliefs. However Terry's family and friends, and his love for them, seem to be a bigger motivator for his activities compared to other bats.

(Granted, I've not seen Beyond in a LONG time, so my words should be taken with a grain of salt.)