Is Docker right for my use case? My company has a system we sell that consists of basically a mini-computer "Smartbox" that is running Ubuntu 12.04. This box runs a Django application plus a number of different upstart processes related to it. Not much else. We have thousands of these boxes out on the field. We manage the package dependencies, process registration, etc. through a deb package with varying degrees of success.

We need a way to efficiently and robustly push updates out to our users out in the field. We also need something that as we upgrade the OS (we are way overdue for a Ubuntu upgrade as you can tell) we can feel relatively secure about our packages "just working".

I don't know much about Docker, but when I first heard about our problem (I'm a new hire), Docker was my first thought. But the more I thought about it I felt like maybe it wasn't, as these boxes are ours we control the OS on it which is a big part of the value proposition of Docker, or so I understand. So if we KNOW our boxes will always be Ubuntu and we basically just have a Django app plus some processes to run, is Docker any better than a deb package?

TL;DR: Docker vs deb packages for a distributed appliance that will always run Ubuntu so platform independence is not that important.
I'm not 100% sure I understand from the question, but it sounds like the Docker solution would be to go from having an (physical?) appliance with an OS and your app installed on it, to having an appliance with an OS and Docker on it, running a single container with your app in it. That doesn't obviate the need to update the OS in the host, and it adds a layer of complexity (and more updates to contend with, as you'll now have to keep Docker and the OS patched) with no readily-apparent benefit as far as the specific areas mentioned in the question are concerned.

However, if you're talking about going from a virtual appliance to a Docker container, that could potentially smooth things out for you, but it also adds Docker as a dependency for your product; you're shutting out anyone who isn't using Docker and doesn't want to add it to their stack just to use your product. You could continue to support those that don't/won't use Docker by continuing to ship the (now "legacy") virtual appliance as before, but now you've just doubled your workload because you have two distributions to support instead of one.