One thing to note is that (last I heard) both Chrome and Firefox sandbox EME modules fairly tightly. Flash is a browser plugin, which means that it usually injects code into the browser itself, and runs with full privileges on your computer, just as much as your browser does. This is what makes Flash such fertile ground for exploits of all kinds, and also makes it bad for your privacy because it has direct access to your webcam, microphone, clipboard, supercookies, etc. — anything the browser can do, Flash can do without asking. If it asks, it's out of the kindness of its heart, not because the browser has any say.

Chrome and Firefox's sandboxes, meanwhile, are both open-source. You can inspect what powers the EME module might possibly have, and know that it can't gain any more. A vulnerability in the code is unlikely to be able to do anything other than pirate your download of Game of Thrones — and that's assuming it even has general-purpose network access. Ideally, a vulnerability would be able to do nothing other than modify the video you see, but the remote site could achieve that by encoding a modified video in the first place.

As far as the general moral arguments about DRM go, it's true that the new boss is the same as the old boss. But the bulk of the EFF's argument against Flash in this blog post is about security, not about open content, and it's important to acknowledge that EME is a significant step forward. The new boss is sitting in a tightly locked cage.