Leaving containers vs VMs aside, docker for Mac leverages a custom hypervisor rather than VirtualBox. My overall experience with it is that it is more performant (generally), plays better with the system clock and power management, and is otherwise less cumbersome than VirtualBox. They are just getting started, but getting rid of VirtualBox is the big winner for me.

When I used VirtualBox for Docker (using Docker machine/toolbox), I would run out of VM space, have to start and stop the VM, and it was just clunky all around.

Docker.app has a very nice tray menu, I don't know or care anything about the VM it's running on, and generally is just better integrated to OS X. For instance, when I run a container, the port mapping will be on localhost rather than on some internal IP that I would always forget.

I don't think he was comparing Docker to VirtualBox.

In Docker 1.11 they used VirtualBox to host a Linux Docker Image to run containers. In 1.12 they switched to Microsoft's Hyper-V.