Brandon Meriweather played 4 years in New England, went to 2 Pro Bowls... he left and never approached his career best tackle or INT totals again, never saw another Pro Bowl.
Players get credited (or overrated) due to team success all the time.
Gilmore never had a season like his DPOY season in New England, in fact he made one Pro Bowl in five seasons in Buffalo. He made 3 Pro Bowls and two All Pro teams in New England. So no, corners never look as good on bad teams as they do on good teams... which makes sense given football starts at the line of scrimmage and works backwards.
Butler's prime didn't end as much as he was exposed for being who he was, good for two seasons and average after that. That's why he was an UDFA, if he was a superior athlete he would have been drafted higher regardless of attending a small school... the same way Jamie Collins was.
Mills and Mitchell will look significantly better assuming New England's defensive front is really good.