According to the OSRS wiki, you get 50% more common loot if you correctly deal with the boss mechanics (The Whisperer page says it pretty much without a doubt). As far as they know there it doesn't seem like it affects the unique drop table.
Right now, it doesn't seem like equipment affects the droprate in a direct manner. Of course, better equipment will probably mean better odds for getting a better/perfect kill. Encouraging players to properly deal with the bosses in this way is a nice incentive to mastering the boss.
Look, when droprates start changing due to chosen equipment or due to other odd requirements, I'll be right there with you on the bandwagon. But getting an extra incentive to master the boss in the form of 50% more
common
loot? I'd say that is a nice way of recognising your mastery over the boss in question.
01-Aug-2023 16:33:12