Tang. I don't see anything particularly impressive about Han's military institutions. I'd argue that it was their leaders that brought them their successes, not the institutions themselves. I'd say their successes make a good argument in favor of the "Great Man" theory.
Sui lasted less than thirty years and bled itself to death in wars with Korea. Nah.
Anyway, while Han collapsed in the wake of the Yellow Turban Rebellion, it took two equally brutal civil wars (The An Lushan and Huang Chao rebellions) to break Tang. Also, An Lushan was a far more formidable opponent than Zhang Jiao, and the war far more brutal. Yet Tang survived, albeit as a shadow of its former self, for almost 150 years afterward.
Finally, Tang kicked so much ass in the West they even got into it with the Caliphate. Sure, Tang lost, but that's got to count for something.
I don't write fanfic, but if I did it would involve Zhou Yu and Zheng He fighting to win the heart of Lai Choi San. Then I'd make them join forces to fight Ming the Merciless, who secretly works for Master Li. I'd squeeze Lu Bu in there somehow.