I think they are all great goalkeepers with few weaknesses, but have different 'super skills' if you like. Neuer is by far the best with his feet, Courtois is by far the best aerially in terms of claiming crosses, De Gea has the best reflexes/shot stopping ability, with Oblak probably a close second to him in that regard.
Of course they are all more than capable of playing the ball out, claiming crosses, making great saves etc, but I'd have a fit Neuer ahead of Courtois for example because I think Courtois is a lot weaker with his distribution than Neuer is in terms of his reflexes. Stick Courtois in at City or Barca and he'd still be very good but you'd be accentuating his main weakness somewhat. Whereas Neuer could be elite at any club.
I agree that their signature strength are in different areas, but I believe all 4 of Oblak, De Gea, Courtois and Neuer would be great at any club. Sure, Courtois' distribution have question marks but so what? At ManCity, for example, he would NOT have the same long passing ability, but as long as he can do short passing, he should be fine. I think he wouldn't be worse than Ederson for ManCity, and ManCity are doing fine with Ederson.
Neuer has had the easiest among these. Again, Ulreich has been playing for Bayern, and I guarantee that most of the world doesn't even know that. Still, Neuer, too, would do great in all other clubs. De Gea and Oblak have had the toughest so far, with De Gea probably edging it. De Gea has played in awful Moyes, and Van Gaal teams and remained world class. He has been a one-man team for them. Even this season, ManU have the best defensive record not because Phil Jones and Ashley Young are great defenders. With another goalie, they let in 10-15 more easily. Oblak plays behind a superb defense, but that defense has been giving away chances in top matches, and he has been a rock behind them.
So all have done well under very different circumstances. I am convinced that these would do well anywhere, and be "elite".