ASP (Active Server Pages) and ASP.NET are both server side 
technologies for building web sites and web applications .

ASP.NET is Managed compiled code - asp is interpreted. and 
ASP.net is fully Object oriented.

ASP.NET has been entirely re-architected to provide a 
highly productive programming experience based on the .NET 
Framework, and a robust infrastructure for building 
reliable and scalable web applications.

ASP:
1) this supports scripting languages,generally scripting 
languages are interpreter based,so execution will be 
slow,and no proper management

2)no server side controls

3)supports inpage technique

4) supports inprocess session

5)uses ADO for database connectivity

6)manual coding to perform validations

7)supports entire page caching towards client side

ASP.NET:

1) supports .net languages.these r compiler based,so 
execution will be fast

2)supports server side controls

3)supports inpage ,code behind techniques

4)supports in process,out process session

5) no manual coding to perform validation

6)supports 3 types of caching
   a)out put caching
   b) fragment caching
   c) data caching

ASP is based on a procedural & event driven programming 
model.. Whereas ASP.NET is based on object oriented & event 
driven programming model.
Application written in ASP.NET are compiled,Whereas ASP are 
interpreted.
ASP.NET can  only support one programming language on a 
page,ASP support muliple programming languages on a page.