A Docker blog post indicates:
Docker containers are, by default, quite secure; especially if you take care of running your processes inside the containe
When you run as root, you can access a broader range of kernel services. For instance, you can:
(It's interesting to note that all those examples are protected by capabilities.)
The key point is that as root, you can exercise more kernel code; if there is a vulnerability in that code, you can trigger it as root, but not as a regular user.
Additionally, if someone finds a way to break out of a container, if you break out as root, you can do much more damage than as a regular user, obviously.