Ho-oh: 1 single Dusk Ball, though I resetted for a good Adamant bird, and on my previous attempts it took slightly longer to catch (didn't took more than 15 balls at worst though).
Lugia: 3 Dusk Balls, then one Heavy Ball. I laughed so hard, seeing as Heavy Ball was useless against Ho-oh. Later I checked the Pokédex and Poké Ball mechanics and noticed why, Lugia gets an higher bonus than Ho-oh, though I probably would have had better odds using Dusk Ball as usual.