Bing has been growing in popularity as a search engine. Google still seems to hold a significant share and we see that with our clients, but I do see Bing popping up more and more. I personally have Bing as my home page on IE and Google as my home page on chrome. I use both browsers frequently. One argument for Bing would be it's cool new features when used with OneNote.
Check out what it can do here:
OneNote + Bing
Great little video showing a real world application.
"Some things are just better together. Bing's new Windows 8.1 Apps can help you research and learn about your interests, and OneNote is a great way to capture things from your life, organize your thoughts, and share them with others. Independently, both are incredibly useful, but when combined, you can really change the way you do things--from start to finish."