Do you want edible berries or seed pods for fruit? Do you want multiple stems or a single stem trunk? Do you want small leaves or large leaves? Do you want to feed birds up close and personal? Serviceberry will get rust and the other usual problems of plants in the rose family. Cankers for redbuds.

Our main concern is with root growth and whether or not either tree's roots might damage our home's foundation (9' away). Thanks!

Redbud's roots are generally deep and should not be a problem that far away. I'm not as sure about the serviceberry, but I think the same is true. Hopefully someone will know.

I doubt both would bother the foundation very much. Why not plant dwarf cultivars so you don't have to prune? Not sure about dwarf servieberries, but dwarf redbuds do exist. 'Little Woody' is my favorite dwarf eastern redbud. Chinese redbud will not grow as large as the eastern redbud, maxing out at about 10-12'. Two popular cultivars of those are 'Don Egolf' and Avondale.

Serviceberry can be grown as a tree or shrub, I would think neither would be a problem with the foundation. Serviceberry is often described as having four season interest, I suppose this is because of the fall color. I have about 6 serviceberries and about the same of redbuds. I have the redbuds along the wood edge with dogwoods for spring showing. I have viburnums and serviceberry near the walkway and garage because I enjoy them more and over a longer period of time. The redbud blooms once and is finished until the next year, nothing much to look at the rest of the year, but the serviceberry has nice fruit and fall color.