I've stated this before and it never hurts saying it again, but the characters act much more like how they are in the original games compared to previous Smash games. The art direction, color choice, new moves and new animations helped a lot in achieving that.
Special mentions:
Bowser - His stance and coloring match how he has been since the early 2000's.
Yoshi - More or less the same as above. Anyway, Yoshi has always been quite faithful to his appearance in his own games.
Luigi - New jumping animation and use of the Poltergust was long overdue.
Toon Link - The art direction does wonders to him.
Pit - This is kind of unfair, since his Brawl self was pretty much made up, but after Uprising, he's become a well-rounded character and all those traits are present in this game.
Palutena - Like Pit, her character became much more established in Uprising and Smash 4 shows it well.
King Dedede - Much more goofier than his Brawl self. The art direction also did wonders to him.
Ike - His look from Radiant Dawn fits his moveset much better and his flames being turned to blue made certain made-up attacks feel more natural to him.
Robin - Pretty much his FE:A self.
Lucina - See Robin.