I am a Flitz user and love it. I get mine from a little mom and pop store nearby. My brother bought a used Marlin .22 stainless that had a little bit of surface rust on the barrel. The Flitz took all of it off. It's great stuff for stainless steel and I like to use it on barrel bores.
I cannot tell you the difference between Flitz and JB's because I have never used JB's before. Sorry.