I'm going to reveal my ignorance here, but in my defense, I'm an accounting major, and I've never taken a computer science class.
I'm about to start a new project, and I'm considering using Python instead of PHP, even though I am much more adept with PHP, because I have heard that Python is a more powerful language. That got me wondering, what makes one programming language more powerful than another? I figure javascript isn't very powerful because it (generally) runs inside a browser. But, why is Python more powerful than PHP? In each case, I'm giving instructions to the computer, so why are some languages better at interpreting and executing these instructions? How do I know how much "power" I actually need for a specific project?
Its an interesting topic and in my line of word I come across this a lot. But I've discovered 'power' in the literal sense no longer has value when it comes to the language. What I fear those telling you 'python is more' powerful are getting mixed up with the language and the implementation.
I'm a recent convert to python (last 2 weeks) previously I was a PHP coder. The libraries made on top of the language of python - namely django -help make the language more powerful - as its faster to use and build upon. 
PHP has the fable 'if you want to do something. there is a function for it' and the documentation is brilliant - therefore powerful in that sense.
And in regards to interpreting the language - again dependant upon who has been coding it - its no matter. By general consensus python may be considered quicker and less CPU intensive, is it creates compiled versions of your code. But PHP can have a good caching system.
In short - Pick you favorite.
What makes some programming languages more powerful than others?