I don't think that's entirely correct.
Brazing is much safer, in so much as a nice looking braze is probably a good braze. But the breaking stress of braze will be lower than that of the parent metal. The upside is the braze is much less brittle, and less prone to cracking.
Welding (lets stick with MiG here for the time being) melts the parent metal, so the join is stronger and more rigid, but also brittler. Also, just because a MiG weld looks nice on the outside, doesn't mean the penentration is necessarily any good.
So, if you were making a chassis (for example) out of tubular steel, and you weren't an experienced welder, I'd say braze it. Another problem though, is that the SVA test in the UK (for small volume car manufacture - kitcars, home builts, etc), they don't like brazing anymore, becuase some beaurocrat in a suit who has never done a days proper work in his life, let alone welded, has decided that the strongest solution must be the best in every case.