Word of advice, the rare loot relic doesn’t affect drops above Blue rarity. So you’d be better off equipping a relic that helps you kill the Banker faster.
The relic does affect drops of all rarity but not by much. It increases the chance that when a white weapon would drop, it’s actually a weapon of a higher rarity. You are technically more likely to get a world drop legendary, but the increased likelihood is tiny, so in practice you’ll just see more greens than whites, maybe some blues occasionally. It doesn’t affect assigned drops, so in farming it is indeed better to have a relic that helps more efficient kills.
I recall reading a lot tests coming to conclusion to the relic only increases chance for rare items to drop as for “rare” as blue color rarity. In expense it makes other rarities 5% less common, likely legendaries included.
You think that’s bad. Try farming quest rewards. Getting a practicable heart breaker took me weeks xD. But good on ya man! Glad you carried through and decided to do the right thing and farm for ten hours (no sarcasm, it may have came out wrong ;). Also its the name of the gun… Just say bitch xD