The most fundamental difference between the two is the language. PHP uses a C-like syntax, while ASP uses Visual Basic as its syntax.
ASP.NET, however, is an entirely different beast; I note you've listed ASP in your title, but ASP.NET in your tags.
ASP.NET is a templating language that can work in front of any .NET programming language, the most common being C# and VB.NET. ASP.NET uses (and comes with) the .NET framework, and is far more object-oriented than either PHP or ASP.
In general, PHP and ASP will seem faster for many tasks, but ASP.NET will provide a better chance at building a robust, maintainable application.
