The Garden of Boboli (Giardino di Boboli) is the more formal of the two, maybe the work is grander: Orchards, Versailles like plantations, huge differences in elevation, buildings housing museums and water.
Of course the police keeps an eye on the place and horses are the only option here. So power to is turned into beauty: a dangerous combination!
The views of the city from the Giardino Bardini however are more stunning. The garden in the foreground also is more intimate. It is a nice climb to get up there, but the reward is beauty. The prize is vision.