This is as old a flame war as the "dino vs. synthetic oil" and "pink vs. green coolant" threads!
We even have MB vs. Lexus, MB vs. Jaguar...and the list goes on!
Do a search and you'll see for yourself.
There are many here that own both MBs AND BMWs, and their opinions are mostly that they do indeed handle differently. Many here contend that the MB is a little "cushier" in handling while the BMW is more of a road car. Depending on personal experience, quality, reliability, longevity and just plain "bang for the buck" opinions will vary for both.
Opinions from owners of both are at best, subjective, no matter what specs you throw at them. This will be true for your friend as well. Brand loyalty will hold more weight when one chooses one brand over another. Again, your friend will fall in this category.
Your best bet is to agree to disagree...even if you could both come back and meet on a closed test track with BMW and Mercedes technicians providing every available model of their respective marques for a showdown, only to have the MB trounce the BMW in every category, you wouldn't sway your friend's opinion in the least bit!