Advantages of ASP.NET over ASP:
Compiled code means applications run faster with more design-time errors trapped at the development stage.
Significantly improved run-time error handling, making use of exceptions and try-catch blocks.
User-defined controls allow commonly used templates, such as menus.
Similar metaphors to Windows applications such as controls and events, which make development of rich user interfaces, previously only found on the desktop, possible.
An extensive set of controls and class libraries allows the rapid building of applications.
ASP.NET leverages the multi-language capabilities of the .NET CLR, allowing web pages to be coded in VB.NET, C#, J#, etc.
Ability to cache the whole page or just parts of it to improve performance.
Ability to use the "code-behind" development model to separate business logic from presentation.
If an ASP.NET application leaks memory, the ASP.NET runtime unloads the AppDomain hosting the erring application and reloads the application in a new AppDomain.
Session state in ASP.NET can be saved in a SQL Server database or in a separate process running on the same machine as the web server or on a different machine.
That way session values are not lost when the web server is reset or the ASP.NET worker process is recycled.
Disadvantages to other platforms:
The server framework runs natively on Microsoft IIS 5.0 or higher and Cassini, a web server developed in .NET (shipped with WebMatrix, a free ASP.NET 1.1 development environment, and Visual Studio 2005); however it can run on Linux on any of the alternative frameworks based on the ECMA standard. The most well known one is Mono Project, a free/opensource framework.
Previous versions of ASP.NET (1.0 and 1.1) were criticized for their lack of standards compliance. The generated HTML and JavaScript sent to the client browser would not always validate against W3C/ECMA standards. In addition, the framework's browser detection feature sometimes incorrectly identified web browsers other than Microsoft's own Internet Explorer as "downlevel" and returned HTML/JavaScript to these clients that was crippled or broken. However, in version 2.0, all controls generate valid HTML 4.0, XHTML 1.0 (the default), or XHTML 1.1 output, depending on the site configuration, detection of standards-compliant web browsers is more robust, and support for Cascading Style Sheets is more extensive.
While ASP.NET 2.0 now produces markup that passes validation, it is debatable as to whether it increases accessibility (one of the benefits of a semantic xhtml page + css representation). Several controls (Login controls in particular, but also the new Wizard Server Control) use html tables to layout components which can confuse screen readers. Extensive use is also made of "inline" css rules (e.g. in the Calendar Server Control) which makes it impossible to fully separate content and styling.
Also check out:
http://www.asp.net/whitepaper/whyaspnet.aspx?tabindex=0&tabid=1