Asking for a link back to their blog is different than re-posting their content -- and there are SEO considerations for both.

A link is one of the most powerful signals Google uses to decide who is a credible source and who is not. The more links, the more credible you must be (so goes the thinking). So website owners are working hard to get a lot of links from a lot of sources. Google has not been shy about touting the benefits of both linking to others AND receiving links. There is issue with Site A linking to Site B, and Site B linking back to Site A. In general, if someone asks you link to them, they may promise to link back, but that link will disappear pretty quickly through automated management.

Sharing the same content is not going to do you any favors. Google is quick to recognize duplicate content and penalize the copy-cats. There are ways around that (with a rel=canonical element), but it is a little more technical than I think you're looking for, right now.

Copying other people's content is done, and sometimes the copier gets more traffic and success than the original poster. There is a good write up of how BuzzFeed does this here: https://www.socialmediatoday.com/marketing/science-behind-buzzfeeds-viral-content

In short, there are reasons to both link to another site and quote their content. For optimal performance, this is measured and balanced with your own content and links coming to you.

I hope this helps, if you have other questions or want more help. Send me a message or schedule a call.

All the best,
-Shaun