What browser is that in, and do you have anti-aliasing enabled in your OS? The 'original' text in your screenshot isn't anti-aliased at all, which I don't think should happen unless you have AA off on a system level.
I'm on XP + Chrome.
What it sounds like the white drop shadow did in your case was simply force ClearType on for that text.
Found a tool that optimizes the contrast http://www.microsoft.com/typography/ClearTypePowerToy.mspx