-with the Defeat clock down to less than 10 seconds, I was able to eliminate all enemy units from the field. The system showed Hostile Annihilation in 10 seconds, but the Defeat clock kept ticking and I ended up losing! Which timer takes precedence? I had eliminated all enemy forces, but he did have more uplinks secured than I did. The game was a Conquest.

I would say the defeat counter. There seems to always be a wait time after the last unit is defeated to give grace to the evacuation process and the choice of the winner to permakill the unit. If the unit was permakilled, I forget what happens.