I use docker for the development of FEniCS, an open source scientific computing package written mixing python and c++. FEniCS requires a lot of dependencies which can be hard to compile (PETSc alike) or need version hold (Boost alike). Docker helps to hold the environment constant. We currently plan to have build bots based on docker as well to streamline build testing.
When I write code inside docker, I always submit to a git repo like Bitbucket. Data persistency is easy. Besides you can always use --volume, which works out of box in Linux.
Vagrant requires some basic shared environment, which is not realistic in my case. For example, I use Archlinux myself and am forced to use old Scientific Linux at work, while many other FEniCS developers use Ubuntu, Fedora, or Mac stuff. It is too painful to write and maintain a Vagrant script for all these (different compiler, boost, blas, lapack and some other 10+ numerical specific stuff). I even tried Vagrant+docker. But in the end, with docker maturing, I switched to docker+bash script instead. It is just more convenient and needs less dependency.
So I'd endorse a docker only approach if you mostly use Linux and your project has a diverse group of people.