He did indeed. He also met an unceremonious end in Jedi. Phasma surrenders because three other people have guns trained on her.
They're both minor characters with pros and cons, and Fett in particular is beloved by the fandom for his cool factor. Is there much point in nit picking over which character was handled better, other than to cite them as a reason to justify criticism of certain films?
Say what you want about either character, how I feel about Empire, Jedi, Awakens, or Last Jedi has little to do with either of them.