I personally find PHP much easier to learn/understand and to get running with more quickly. Because ASP is now really part of a greater framework (.NET), it's more complicated to set up and use.

The people behind PHP are working hard to make the language more robust, with more object-oriented programming features and development frameworks that will work with PHP. But the underlying roots of PHP are easy to grasp, and you can start making use of its simpler features quite quickly. Plus, there's tons of support for it, and plenty of open-source software you can use with PHP.

Both languages can do most things you're likely to want to do if you're publishing websites. There are advantages to using a framework like .NET for web apps, but as a web publisher I haven't come across a problem I couldn't solve with PHP.