TL;DR - Yes, you should use both for better CTR in SERP and Social Networks.
OpenGraph is described here:
http://ogp.me/
and OG is mostly used from Facebook and G+.
Twitter used TwitterCards:
https://dev.twitter.com/cards/getting-started#opengraph only for them.
G+ used shema.org or OG:
https://developers.google.com/+/web/snippet/
https://developers.google.com/+/web/snippet/article-rendering
Pinterest used RichPins:
https://developers.pinterest.com/docs/rich-pins/overview/
So you should read excellent article from Cyrus Shepard about all meta tags:
https://moz.com/blog/meta-data-templates-123
where everything is described with examples.
And answer is YES! Today is 2015 and within few days will be 2016. Today shares in social networks are so much important than also baclkinging. Of course organic visits and visits from social networks are different, so you need to implement both of tags to get maximum performance there.