There are some cases where picking between the Raspberry Pi and an Arduino are easy (like when Linux is involved), but oftentimes it's hard to make a choice between the two. Make came up with a simple question to help you decide.
Obviously, this is a complex topic with a lot of variables, but Make came up with an easy rule of thumb:
Think about what you want your project to do. If you can describe it with less than two 'and's, get an Arduino. If you need more than two 'and's, get a Raspberry Pi.
It's a pretty good rule of them, all things considered. It's often hard to figure out just how complex a project needs to be to need a Pi, and this a good place to start.