I'm torn on this.
First and foremost, I think he's fixated on the throne. He actually does come across as quite narcissistic and self-centered from a lot of his actions throughout the Civil War (both sides), and he seems to only "care" about Nord traditions when they serve his ends. He's a great orator who can motivate thousands of people to die for him so he can have the best title and the most awesome chair. He's knows exactly what buttons to push and how much pressure to apply to motivate people to serve his purposes. He understands it's better to be feared than loved, which is why his act of regicide is designed in such a way as to instill terror in the Jarls so they'll be too scared to oppose him in the Moot.
However, I also do believe that he is fighting for what he thinks is right, and I do think he actually cares about the people under him and the cause they fight for.
There's also the matter of redemption. I think a lot of what he's doing is to right his past wrongs. Abandoning the Way of the Voice, selling out the Empire to the Thalmor, failing to keep the Thalmor out of Markarth. He's a man whose legacy is a long list of failures, and I'm sure the separation from his father has compounded his problems, making him fret over his father's legacy and whether or not he can live up to it.
Had it not been for the bs "You're either with us or against us" attitude that the developers took when designing the Civil War, I'd be on the Stormcloak side, or at least actively against the Empire's. Ulfric's good at leading men, but he doesn't seem to be able to administrate worth a damn, something I doubt will get better after the Civil War ends, considering that not only will the territory he's in charge of increase considerably, but he'll probably be most fixated on gearing up for war with the Dominion.