Some plugins load things from other sites on the client side via AJAX or an IFrame. You see this for things like Facebook and Twitter plugins a lot, as well as some RSS feed reader plugins. Google doesn't tell us exactly how they process everything but in these cases it probably will not index that content as part of your own site, because it relies on the browser to assemble all of this content and it's visible to Google that those parts are not coming from your own domain.
HungryFEED, by contrast, pulls in the data on the server side and embeds the feed content into your page. So in this case the information really does become a part of your site. It should be indexed by Google the same as static content.
As far as how much page rank you gain, that is a more complicated question. Technically you are duplicating content that comes from another source. You would think that Google will favor the original source of the content. But it probably depends on the topic of your site, what kind of page rank you already have, etc.