Both are also often considered great characters in their own right in their respective fandoms despite having less screen time then other characters. As I said before, Batman actually has less screen time and development in the Batman The Animated Series then his Rogue's Gallery and Companions. Same thing with Asami, she tends to get less screen time then Mako or Bolin and the villains of each season. And yet, both are seen as some of the best characters in DC and Avatar because, as Chuck said, when you're forced to limit how much you use the character you have to make their every scene count.
Despite having less dialogue then Mako or Bolin Asami has a lot more depth then either of them, IMO and most of the time that's just conveyed through her expressions and body language. The way she struggles with herself when her father reveals his true nature and her debate with herself when she is forced to choose keeping her only remaining family and doing the right thing. The glare she throws at Mako when he decides to dump her in favor of getting back with Korra, or the way she holds herself when she talks with Varrick and how she deals with him as the series goes on.
Same thing with Bruce as shown in, let's be honest, every episode of BTAS we see what he's going through just in how he acts. The way his face falls whenever he feels that he can't give enough money to the poor in The Forgotten, the glare he gives Ferries in Heart of Ice or the way he smiles when speaking with the actor of The Grey Ghost.
Both tells us so much about themselves without ever saying a word. And finally, the two are utterly committed to the side of good despite all the crap they get put through. Asami has never once wavered from helping Korra in her quest to bring Balance to the world while Batman usually never wavers from protecting Gotham and the rest of the world.
So, in my humble opinion, comparing Asami Sato to Bruce Wayne aka Batman is pretty accurate and both are great characters.
