Does anyone know of a script that does both? I see tons of regular auction and reverse auction scripts, but I haven't been able to find one that does both things. I prefer free, but I'm willing to pay if necessary.
You can check this solution for Joomla CMS http://www.thefactory.ro/shop/joomla-components/auction-factory.html
I highly suggest you use to www.ajauctionpro.com AJ Auction Pro is the best Auction Portal script software available in the Universe. Being a PHP /MYSQL Script providing complete online auction solutions, it has now expanded to offer services such as Merchant Solutions, Packaged Software and Enterprise Solutions. Hope this will help you! Good Luck!
You can get AJ Penny Auction script or AJ Auction 2012. both scripts offers you reverse auction, and regular auction facilities. All these scripts are easy to customize for your need.
Use Wordpress with this Sitemile plugin (check the demo!) http://sitemile.com/products/wordpress-auction-reverse-auction-theme/ Wordpress is easy to use, friendly and very stable (used on millions of sites) and constantly under development.
I am a huge fan of the Ajaxphppennyauction (do a google search for the result)... Aaron, the owner is very helpful with any requests or questions you may have.