
Compared to a deciduous tree that drops its leaves every Fall, my experience is that bamboo is a 'cleaner' plant'. Why? Bamboo tends to drop culm sheaths (a large one from a Bambusa oldhamii 'Giant Clumping Timber Bamboo' is pictured above side-by-side with my hand), some leaves from the plant (they shed and renew leaves throughout the year) and some dead branchlets that fall off cleanly at the nodes.

Based on my observation in my yard (looking at the row of non-deciduous Photinia bushes we have along the fence) and seeing other similar plants used for privacy, bamboo is equally, if not less messy than the average bush or tree used for privacy.
Bamboo leaf litter drops close to the base of the bamboo plant (most bamboos are pretty column-like in growth, compared to an average tree that tends to grow in a triangular form). Also, tree leaves are lighter, generally speaking, and are easily carried in the wind to areas of the yard where they are not wanted.
One item to note on leaf litter from bamboo, is that it is actually good to leave bamboo leaf litter at the base of the bamboo plant because that leaf litter contains a small amount of Silica which is important for the growth of the bamboo. In a sense, the bamboo plant is re-feeding itself an important element to its long-term growth - Silica.
Is bamboo mess-free? No. But, in my observation over the years it is equally, if not less messy, than many of the common trees and bushes used for privacy, plus its a much more interesting plant. Not that I'm biased...
Cheers!
Sean
Mad Man Bamboo
(916) 300-6335
Mad Man Bamboo on Twitter - @madmanbamboo