I have only done Infected all the way through, but it certainly took enough tries that I learned all about bringing down Borg!
I carry multiple weapons of different types, both in energy and function. My choice of which to use depends on team makeup and our strategy.
The reason you carry different energy types is because the Borg may adapt to (for example) your phaser, but you can quickly swap to your antiproton weapon and keep fighting. It gives you a lengthier period of damage output before having to remodulate your weapons. You can also use a melee weapon, which is unaffected by the adaptation mechanic.
Quite honestly, my experience has been that any weapon type works quite well up until the final encounter. In the Rebecca Simmons fight, I found it most useful to carry a sniper rifle and a knockback weapon (like a blastwave or high density rifle). The sniper rifle allows you to snag Borg who may be on distant platforms, and the knockback weapon lets you simply blast them into the plasma pool.
As far as I know, the debuffs take. Knockback certainly works, I can say from first-hand experience.