Thompson's shot-making abilities are historic. The idea that he's just good for open catch-and-shoots, like a Kyle Korver, is way off the mark. He's capable of knocking down heavily-contested threes, hitting threes off the dribble, shooting fade-aways out of the post (a shot that's unguardable and was the province of players like Jordan, Kobe and McGrady). He's added a competence at driving past defenders trying to close-out on him and either attacking the hoop or finding an open teammate, even if he's not an elite slasher. He's become a superior version of Reggie Miller, except with much, much better defensive ability. The numbers for James Harden and Damian Lillard against Thompson's defense were particularly brutal.
The warriors play great team defense, I don't think it's so much Thompson's a great defender as they are just all really good at playing defense as a team.
I think it's both. Scheme alone isn't enough--it requires talent. Green, Thompson, Iguodala are all great defenders (though Green and Iguodala are on another level from Thompson), Durant has his moments and Curry is a technically proficient defender who's good at playing to scheme. They play a smart scheme that is based on their abilities.
Klay is a better version of Aldridge, in that if he's your best player, your team is fighting to make the playoffs. If he's your 2nd best player, then you've got a chance to compete for a top spot and maybe make a run. If he's your 3rd best player, then you have the chance to win titles (and apparently have a dynasty!)