If you're going to use scripting in web pages, and don't have control over which browser is used, you HAVE to use Javascript, since only IE supports VBScript.]
For Windows Scripting Host scripts, it's a matter of taste and preference. I use VBScript for scripts to run on my computer, but Javascript in web pages. VBScript isn't case sensitive, so you don't have to worry about capitalization (or the lack of it) like in Javascript. Javascript does objects MUCH nicer than VBScript, so if you're familiar with object-oriented programming, that'd be the best choice. It's much easier to simulate database records with several fields with Javascript (using objects) than VBScript, I think.
Both can access WSH objects with equal ease and power. If you're used to Visual Basic, or the old QBasic, then you'll feel fairly at ease with VBScript. If you know C, C++, Java, or one of the other C-based languages, you'll find Javascript more comfortable.
I like some of Javascript's string handling functions better than VBScript, but VBScript has more flexible popup message boxes. Each language has built-in functions that the other doesn't, but those would be easy to develop yourself once you knew the language.
The answers you'll get to this question will probably be more subjective than objective, and based on what the programmer was originally familiar and comfortable with.