Yet they have some privileges a normal script doesn't have, for example the ability to post messages to parent extension which can be exploited.
$(element).html(user input);
UPD: I was wrong, jQuery inserts a script tag into DOM instead of directly calling eval() so the code above is not equivalent to eval and is another type of vulnerability.
In the context of an extension manipulating a web page, though, the jQuery thing you quote will evaluate the script with the permissions of the web page, not the permissions of the extension. On the other hand, doing eval() with a string from the web page will evaluate things with the permission of the extension.
So there is a pretty subtle (and irrelevant in web pages!) but important distinction between the two kinds of script injection here. In a web page they are more or less equivalent in terms of leading to XSS if you have untrusted input. But in an extension, the jQuery one is OK if your input comes from the web page itself, and the eval() version is not.
[Disclaimer: I work for Mozilla, but not on extension policy.]
For example: arbitrary user input from a web page is passed to the addon. Angular handles it, and does "eval-like things"[0] with it. Now the attacker is running arbitrary code in a privileged environment.
[0] eval-like things is a core part of how Angular works. So the vulnerability doesn't necessarily apply to Angular 1.x in a normal web page. But it wasn't designed to be run with higher privileges.