They get big. We had red (berries turn black when ripe, but still considered red) ones when I was little. The fully ripe berries are very sweet, but the flavor is not very complex, so some people find them bland, even though they are sweet.
I would stick with the red, but that's because it's what I know. From what I've read, the red is native to America, while the white is from Asia. They will hybridize with each other to create pink berries. I just think it would be weird to eat pink or white berries, because growing up, the trees young berries are light colored and turn from white/greenish, to pink, to red to black. Only the black ones are worth eating, the unripe berries are very tart and will make you sick.
Even though the trees get big, ours always had low branches that produced plenty of fruit within jumping or climbing distance. And, if all else fails, there's always a ladder...