If you want privacy, write a letter if you are in the US. In other countries, even that probably doesn't work. You want privacy, you have to opt for a cave (not The Cave).
I haven't used Chrome. I am sure it is capable, IE is used a lot for Enterprise Applications as all browsers don't operate the same.
Most companies standardize on IE for support. When I go to a company, that is the first question I ask, what is the company browser. That is the only browser we will test and support (browsers are almost as bad as an OS).
Firefox, I use it cause it has been an old war dog and was the first (Netscape). I paid $40 for the first Netscape back in 93/94 (sometime around then).
I know I am being tracked. Even your searches are being tracked. All in the name of security and better user experience. And Jimmy probably does know what browser you are using. I know those capabilities has been around for 6-7 year. First thing that is done when a page is loaded is browser detection to know how to route the code (If this then, call, etc.).
As long as you are on the net and really understand how to server hop, use IP alias and all of that cyber trolling (even that it is only good until the government decides it wants you butt, and then they will find you).
So just relax, big brother is watching, just don't give them anything to see.