I'm not sure they'd lose the war either. The navy fielding swarms of <1000 ton ships would have to have overwhelming numerical superiority every time they had contact with the enemy. The attrition math would have to be in their favor even when they faced system defense fleets and system defenses. If they would lose battles, an offensive capital ship fleet could cut through their defenses and systematically destroy every high value target (industrial centers, shipyards, etc.). The swarm fleets would have to either group up to have the attrition math in their favor or disperse into smaller fleets to attack many lightly defended targets. risking their attritional superiority.
It becomes a contest of resources and industrial capacity. The navy fielding the <1000 ton ship swarm fleets would have to have such an industrial and resource advantage that they could build numerous-enough swarm fleets that they could either take down fleets with capital ships + escorts or attack in so many places at once that they can do enough damage to end the war before the capital ship fleets could stop them.
If the two navies have roughly equal industrial capacity and resources, it would be something like pitting 10,000 infantry against 8,000 infantry with a strong artillery component. Or, 10 million <1000 ton ships against 8 million <1000 ships + a capital ship group with each <1000 ton ship fleet. It would be dicey at best.
In Traveller, it would all depend on how the space combat rules work out the attrition math.