I've been using the two services pretty extensively lately and all the while doing my own non-scientific analysis of why and when I choose to use them.
Google, I find, gives me far better results when I am looking for science or engineering related searches. More often then not if I have a technology question I'll get good results from Google.
Bing feels like it's more geared toward business, people and images. I don't know if this is what Microsoft was aiming for but that's when I decide to Bing it.
Apparently now I'll also have to consider when I Facebook it - but that can wait.