The TMNT work pretty well in a contemporary era, other superheroes not so much but it depends on a case by case basis but in general the less technology that is available the better any superhero operating seems more plausible.
I also cringe when you have some old franchises with modern technology and it doesn't work, first example to come to my head is the Simpsons, now that is a show that I totally base as existing until the early internet so anything that is more advanced than a 16 bit console doesn't mesh well.
Turtles on the other hand
had an iphone since the old toon and were always ahead technology wise so making it more umm... ok.