One of the nice features of the policy list is that you can put your server on it in testing mode. In testing mode, any failure in TLS negotiation is logged and reported, but the message is sent over the insecure communication. So it shouldn't cause any breakage.
To sum up from that post, we think STARTTLS Everywhere is a stop-gap measure until DNSSEC is fully deployed, and STARTTLS Everywhere can act as a preload list for MTA-STS (to prevent DNS downgrade attacks).
One major difference is that Privacy Badger doesn't use a blacklist like the others and really isn't designed for the purpose of ad-blocking. It's designed to prevent non-consensual tracking, so it observes which third-party domains try to store high-entropy cookies, and if it sees a third-party domain doing so across multiple first-party sites, blocks any further third-party requests to that domain.
Full disclosure: I work at EFF, which makes Privacy Badger.
That's correct; Privacy Badger doesn't block anything by default because it doesn't use a blacklist. Instead, it observes the behavior of third-party domains and blocks them based on their behavior. (So it may take a bit of normal browsing before it starts blocking things.)
Also, Privacy Badger recently transitioned from beta to 1.0, so if you last tried it more than a month or so ago, I recommend giving it another shot. And if you find bugs, please report them!
Full disclosure: I work at EFF, which makes Privacy Badger.
NoScript blocks Javascript/Flash/etc. based either on a list you import, or on a case-by-case basis. I use it as a security measure, blocking potentially harmful content by default and enabling it only if I need it for the site to function.
Privacy Badger is not designed for security so much as it is for protection against non-consensual tracking. It observes which third-parties store high-entropy cookies on your device. If it sees a third-party domain doing so across three different first-party websites, it automatically blocks requests for any content to that third-party from your browser.
So I'd say the big differences are Privacy Badger is set-and-forget, while NoScript isn't; Privacy Badger protects against different tracking (including pixel tags); NoScript protects against some first-party tracking (if you don't allow JS on a first-party domain) and security dangers.
Full disclosure: I work for EFF which makes Privacy Badger.