Canonical and No Follow tags
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Both pieces won't be ignored, just one will. But you do need to do it, either that or rewrite the content on one so it's no longer duplicate.
Here's what you're looking for anyway
http://www.seomoz.org/blog/canonical-url-tag-the-most-important-advancement-in-seo-practices-since-sitemaps -
It is my understanding that canonical tags help prevent duplicate content by telling the crawl bot where the original content exists. Say I want to repost an article from Seomoz on my site that I think my readers would find useful. If I did this without a canonical tag Google would penalize me for posting unoriginal content. To avoid this I would include the original URL back to the Seomoz post in canonical tag to tell Google where I am getting this content.
An internal example would be on pages that include URL parameters (pagers for example: www.example.com/product-page and www.example.com/product-page?page1. Here you would want to include a canonical tag to the clean URL).
I believe nofollow tags alone don't help with duplicate content issues. You need to also include a noindex tag. Combined, this is an aggressive and effect way to keep duplicate content out of Google's index and avoid penalizations.
Hope that helped explain things a little better!
Andrew