Back when I played Emerald, I had embedded into my head that Premier Balls had a higher chance to catch legendaries, solely based on the fact that I caught both Groudon and Kyogre in Premier Balls, haha. Of course, by Gen IV, I learnt that was false. But, in the back of my mind, I feel like I should always carry Premier Balls when catching legendaries. (funnily enough, I have a dedicated box full of legendaries that have been caught in Premier Balls.)