As much as I really like WooCommerce, it can be a (very) heavy / overcomplicated solution for a simple digital downloads store. There's less code being added to your site with EDD, so there's less of a chance for issues to sneak up on you. You might also see a performance benefit too. If the payment processor you'll use is also already supported right out of the box, EDD probably is the way to go. For "enhanced" EDD theme support (unless you're building it by yourself), you may be limited here.
However, WooCommerce has a more diversified extension library and usually is supported out of the box by many Themes. So, if there's an essential feature you need that's not offered by an EDD add-on but is already available in WooCommerce (the core plugin or an extension) then you might be better served by WooCommerce. WooCommerce is more geared towards virtual / physical items but works pretty well for downloads too.