First of all, both are free! Visual Studio Community Edition is newly released today.
Are two main differences between Visual Studio 2013 Community Edition and the Express Editions
1) Visual Studio Express Editions are targeting specific platforms: Express for Web allows you to develop Web apps; Express for Windows allows you to develop Windows apps; Express for Windows Desktop allows you to develop desktop apps. But with Visual Studio Community Edition, you can develop projects targeting cross-platforms.
2) Visual Studio Express Editions do not allow users to use extensions (aka. plugins). There are over 5000 great plugins for Visual Studio in Visual Studio Gallery. Plugins such as Developer Assistant can boost developers’ productivity. Unfortunately, they are not available to Visual Studio Express users. With Visual Studio Community Edition, you can access and use All !
Visual Studio Community Edition may retire Visual Studio Express Editions in future, but this is not decided yet.