We're only talking about one link here, right? A link from one site to the other and from the other back to the first? Do it. It's not a problem. It isn't as though you're setting up an entire link farm to generate false impressions.
I have 4 sites that all rank in the top 5 and the first link any of them got was from my existings sites. I don't put the links on the home page, but usually on the About Us (because it makes sense to explain that site B is owned and operated by site A) and/or on the Contact Us page.
Duplication of content is a huge 'spam' issue with the search engines so it is important that you take all steps to not duplicate content.
I have a different opinion about this. What happens (with Google anyway) is that the original site that lists the content gets "credit" for it and will be ranked accordingly. Other sites will not be penalized as spam but will usually be ignored. This however, does not apply to articles.
You can find the same article listed on countless sites all listed one right after the other in Google SERPs. Doesn't seem to matter how many sites they are on. Type in "The Mystery of the Magical Keyword Density Formula" (for example) and you'll see it pop up in the rankings on I don't know how many sites. Same, exact content word for word and yet all those sites have their pages listed in Google.