This question cannot be answered; since, it depends purely on the programmer and their preferences. (Bit like the Mac vs Windows arguement) each have their own strenths and own weaknesses and based on those, you should make your own decision.
Seriously, this is a question you won't get a definite answer to. I think both are good. PHP for me is better since I know it :-) (or at least I think I do). As far as I know PHP has more installations worldwide. An not to forget, PHP is open source.
There used to be a tendency for asp.net sites to be more expensive to host, but I think this has equalised by now. As other contributors have stated, there is no 'best' choice. Like many other questions, Windows vs Mac, iPhone vs Android, ObjectiveC vs Java...
From my own experience, PHP is very accessible to the new 'coder'. You can get it up and going without any knowledge of Object Orientated Programming and do everything 'procedural' style. This is both a strength and a weakness. The weakness bit due to the ability to code badly and still get it to work, which develops poor skills and bad habits. If you do go down the PHP route, get into OOP as soon as possible once you get familiar with the native functions. The 'basics' are pretty common to all languages, where you learn about variables, constants, arrays, native and user-defined functions. Learning to programme in any language therefore, will be valuable, regardless of whether you later decide to change to a different one.
To get a taste of each, see some quality online tutorials and see how easy (or difficult) they are. You could even write the same simple program (with the help of aforementioned tutorials) in each and compare them, e.g. a basic blog.
The language you choose should also have a choice of quality IDEs. Both PHP and ASP have these in spades, although the better ones will require payment.