ASP.NET and ASP.NET MVC are actually completely different (even though they share the same name) - ASP.NET MVC is an MVC framework, just like Rails (and Django, mostly), whereas ASP.NET is component-oriented.
I would use ASP.NET MVC over ASP.NET for any web project I had to build using .Net.
I would use ASP.NET MVC over ASP.NET for any web project I had to build using .Net.