Everyone focuses on McConaughey and he's done a SUPERB job for sure, but since you're all rewatching the show again anyway pay extra attention to fucking Harrelson's range and subtlety throughout the show so far.
I don't know, I think they went in opposite emotional directions and both did it great. At the start, Rust is withdrawn and pretty much a mess being held together thinly. He's got this super pessimistic view of the world due to losing his kid, but he's not really sure of it; he even says when Hart asks him why he wakes up and does the job if it's for nothing "I'd like to say I'm bearing witness, but really it's my programing."...So Rust says this stuff, but you can tell he isn't sure of himself, he won't commit to this view. And then you have Hart, who is absolutely sure of himself. Family, old time religion--good old boy. He knows what a man needs to make his life worth living and he walks around with confidence because of it.
However, as the story progresses and things get more fucked up? They go in opposite directions. Rust becomes more confident, more sure of himself. It's like everything he is seeing is 100% confirming his world view and he knows exactly what he has to do. Meanwhile, Hart starts questioning things, like whether he's a bad man; he loses his marriage and he kind of self destructs, until at the end of Episode 5, Rust is essentially the shot caller. It was a pretty neat emotional swap as they both descended into the seedy, "evil" world just under the surface of world everyone sees.
On another note: I'm more and more convinced the murders were done specifically to catch the attention of a "true detective" (Someone smart and resourceful enough to follow the trail). When you hear Rust talk about it, he says things like "this guy is a meta psychotic" "he is articulating a vision"...Then he finds the little devil nets in areas he's investigating and he says "It felt like someone was trying to have a conversation"....Then he tells Hart "This girl was just like chum in the water." It really made me think that the trail to Lodeux was set up, and heck, maybe Lodeux knew he was a sacrificial lamb; so whoever is behind it could have a conservation with a "real" hunter: which would undoubtedly be a perfect priest to learn his grand "lessons".
I don't know who the Yellow King is, but it seems like whoever he is? He's the one hunting, not being hunted.