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?
I hate statements of the sort "language X is more powerful than Y." The real question is which language makes you more powerful. If language X allows you to write better code (that works) faster than Y does then, yes, X is more "powerful". 
If you are looking for an objective explanation of language powerful-ness ... well, good luck with that.
What makes some programming languages more powerful than others?