There are no duplicate content penalties, as such. Google will crawl both articles and decide which it thinks is the original, and index that one, but not always both.
If you're publishing the articles to your site and Ezinearticles at the same time, there is a danger that Google will find the one on Ezinearticles first and not rank your page, believing yours is not the original.
I would recommend writing unique articles for your own site if you can, that way, there's no issue of duplicate content. I know that's probably not the answer you want to hear, but these shortcuts and time-saving plug-ins may seem like a good idea, not they're not the best way to go about creating great content for SEO.