I’m pretty sure @lowlines basically confirmed that the only thing affecting boss legendary drops is RNG and difficulty - and difficulty only as in some gear only drops on advanced.
Not sure how Loot boosters play into this. I haven’t cared enough to check…
Loot boosters only give you loot packs from finishing matches, they don’t affect drop rates within the actual level. The more people in your match with active loot boosters, the more packs you get on the results screen. Winning with 1 booster = core pack, winning with 2 boosters = core pack + faction pack, winning with 3 boosters = epic pack + faction pack, winning with 4 boosters = core pack + epic pack + faction pack, winning with 5 boosters = core pack + epic pack + commander faction pack with a 1/6 chance the commander faction pack is a legendary pack instead (the third pack is randomly drawn from a pool of 6 possibilities, each factions commander pack plus legendary pack). If you lose, it’s just a common pack no matter how many boosting.
Some legendary gear only drops in advanced difficulty. However I’m pretty sure the chance for a legendary to drop is the same. For example a boss will have a chance to drop a legendary and it will be either gear A or gear B on normal and either A, B, C, or D on advanced. So if the piece you want is not an advanced drop then you are better off farming on normal because the pool of gear is smaller and you can clear it faster. Hardcore makes no difference except on score I think.