Pachyderm does use Docker under the hood, but we don't obfuscate it away, so Data Scientists get the full power of Docker (and most of the power of Kubernetes) at their fingertips. This means you can easily grab prefabricated environments such as Jupyter or Tensorflow container images and deploy them directly. Docker is so good for packaging environments we didn't want to conceal it.
On the other hand, we felt the data orchestration capabilities of Docker were pretty lacking for Data Science use cases, so that's where we've focused our energy. Volumes are a good basic tool for getting data to your code, but they're a pretty blunt instrument. How do you split data up to parallelize over it? How do you make sure you've got the right version of data? How do you schedule new computations when data becomes available? Those are some of the use cases we solve with our distributed file system PFS.