Hi,
When we use Publish utility to deploy the website, the classes in App_Code will be compiled into dll and be placed in Bin folder. So I think it is few differences with using external Class Library while running it on server.
But there are many differences in development, reusable, team work, etc. For example, if we put all the classes in the App_Code folder, this will enhance compiling time, instead, using separate Class Library will improve build performance.
Commonly, if it is small website (simple operation on Database), we can put all classes in the App_Code; if it has many functions in DataAccess and Business, we will use Class Library. So you can choose which manner basing on your requirements.
You also can refer to http://weblogs.asp.net/bradleyb/archive/2005/12/06/432441.aspx
I look forward to hearing from you.