Most metals oxidize (rust) and are able to bond very easily with other elements that change their appearance (fingerprints.) To clean a cymbal, we strip everything off the surface. IMMEDIATELY, you want to seal the fresh metal before handling it again. Use simple Car Wax Mist Spray and buff to a nice shine. It won't effect the sound, and prevent fingerprints. Easy to maintain too.
I have tried car wax, it looks more shiny and makes the sound drier, but a year later the color turns black faster, in my opinion, the best thing is not to give any coating to the cymbal that has been cleaned, the best way is to keep the room temperature and humidity good for studio
I love using both products however, if you look closely the Barkeeper's Friend along with your scratch pad left fine scratches. Also you should have used water to clean off the Brasso for a fair comparison.