Okay, let's assume that, in the former case, the functionality required is built into the browser and enabled by default.
The problem with the former case, then, is that I get a browser that ostensibly supports my freedom, and this code that runs things secretly, without letting me intervene or analyze, comes in with it, under the radar.
In the latter case, I have to take a deliberate action, explicitly agree to a license, and install a product I know to be freedom-denying. So I have something icky on my computer if/when I specifically choose to, and I know exactly what the icky stuff is, why it is there, and how to get rid of it if I decide to.
I think it would be much better if Mozilla were to present the DRM stuff as an optional, not-installed-by-default plug-in with clearly restricted scope, access, and capabilities. If they do this, then they probably ought to spin off the group that makes the plug-in as a separate organization.