I make hundreds per day from articles and have joint ventured with some of the best article marketers on the planet, so I do know my stuff about it.
Here's what I do when it comes to article submission: 1) I send out my articles to the top directories first (Ezine Articles etc) 2) After two weeks, submit your articles to other lesser known directories Step 1 is for generating direct traffic and getting your articles ranked in the search engines.
Step 2 is for eking out that little extra traffic from posting on the lesser known directories, and is not necessarily for SEO purposes.
(one way to speed up this step is to use an article submission service like Article Marketer or Submit Your Article) Google will take the article that you have on the article directory with a higher Page Rank, and give that priority.
So yes, duplicate content will affect you, but it will only affect those articles on the lower-tier directories.
It will have no effect on your article on the top directories, because you submitted it first.
Google will take that as the original article that you submitted, since you it in first.
So do both, but proceed with the top-tier directories first, hold off for a while, then submit to the lower-tier directories that don't get much direct traffic.
The purpose of step 2 is just to increase your traffic gradually and not for SEO purposes.
Unless of course, you're looking to build backlinks for your site, then that's another story altogether!