ASP and PHP are both programming languages that are commonly used to create websites. Unlike the usual static html web pages, ASP and PHP websites are more dynamic and can allow users to interact and exchange information using the website's databases.
ASP is the short term for Active Server Pages, a type of program that works with Microsoft alongside IIS or Internet Information Server. ASP needs a Microsoft Server for the website to work. On the other, PHP or Hypertext Preprocessor, runs using Linux or Unix server. The more updated PHP programs can now run on an NT server.
PHP programs can also run in Windows, Solaris, Unix and Linux while ASP can only work with Window-based platforms. Just recently, ASP can now run on a Linux platform given that there is an ASP-Apache program installed on its server.
When to use ASP/PHP:
Features, Security, and Extendability are going to be more or less the same. What can be done with PHP can be done with ASP.NET.
Frameworks — Again, when it comes to features of frameworks, it will be more or less the same. However, being more specific than the language itself, you'll want to consider:
What your developers are most comfortable with. Knowledge = efficiency.
On a project-by-project basis, one framework in one language might be a better natural fit than a framework in another. Being more specific than the language itself means a framework cannot help but be well-suited to some tasks and less-well suited to others.
Average Development Time — Your average development time for a very small project might be better with PHP since web hosts are so easy to find and dev machines so easy to set up. However, with anything bigger, as long as you have good devs, or are already set up for either, it will probably be a wash.
The main consideration you should make is what technology stack your client wants to be tied to going forward. Neither mixes well (easily) with the other. They may have developers who are familiar with one or the other.
If your client likes the idea of being connected to Microsoft, then go with ASP.NET. Some clients will have more comfort regarding future support, upgrades, etc. with MS.
If they like the idea of open source and Linux servers, go with PHP. This may interest some clients due to transferability of web hosts, free software, etc.
And lastly, if they don't care, then go with what you are most comfortable with. There's not much to it beyond that.