I wrote an article and posted that on my site, but at the same time I also submitted that article to a few directories. I'm pretty sure they got spidered first, will the search engines now see mine as duplicate content and not bother with listing it in their results for the target keyword?
try to submit just a summary of your content and make a link pointing to the main content... or maybe let it index first before you submit, besides its easy to get index these days...
It doesn't matter who's indexed first, it's the authority of the page and anchor text pointing to it that determines which version ranks. As both above said, either submit a condensed summary or completely different material to other directories than what's on your site.