My research stations take up 12 slots? Indeed, they do. At three labs of military tech, you should be significantly more powerful than a max research enemy of any other side. It's not that your labs take more slots, it's that your research tree goes oh so much further than any other side. One of your primary enhancements is antimatter, an indescribably helpful upgrade. You'll find that your abilities, for the most part, have absurdly short cooldowns you can't possibly utilize.
The tricky part to losing shows up when you actually can utilize them, because you have 300% extra antimatter to play with. An Assimilation Cube only has 250 antimatter at level 1, and only gains 20 per level. With max research, that's a thousand at base, and 80 per level. Continuous ability usage for brief periods of time leading to massive devastation of a 40 ship fleet. If it has a high level queen preventing it from being disabled and a few supporting cruisers, you should expect the AI to throw a thousand fleet points at it before much in the way of damage happens. Once you have multiple high level Borg Elites at anything near max research, the game should be over.
The Borg have an ability for upgrading assimilated ships, "Borg Collective" is on the Borg's shipyards and the Advanced Sphere. When the Borg take over a ship, any loss of stats on its part means you have terrible research parity with your enemy. Borg research is massively better in hull and antimatter regeneration, but they have no parity with shields and weapons from the other races. Once you buff them, they will destroy, with great ease, their unassimilated counterparts.