From my perspective, where I'm planning a hosting service with multiple customers, containers promise to allow me to slice machines into dedicated chunks. VMs could do this too, but they'd consume far more disk-space, which would mean my hosting costs would be comparatively higher.
Containers promise to allow me to limit the resources each of my customers can consume without killing the entire box. For example, I can limit RAM, CPU and disk-space per customer. If one customer goes rogue, the shared box remains performant for my other customers. Also there's the data protection: in theory customers would not be able to access each others' data, even if they tried to.
There are other considerations as others here have pointed out. This is just my primary concern at the moment.