To clarify, I think Terry is a great Batman.
But Dick Grayson had a much bigger, much longer, much more satisfying arc to become Batman.
I always loved the idea of Dick Grayson as "Batman done right" according to Bruce's own testimonials. "Did you raise him so he'd turn out like you?" "So that he WOULDN'T."
The DCAU version, as much as I ADORE the DCAU, botched this HARD. Dick Grayson never had a falling out with Batman in the comics; Bruce was his father, for all intents and purposes, and Dick was every part of it Bruce's son. Bruce saw the tragedy of Dick's childhood and saw the cycle repeating, so he stepped in to guide it and avoid the mistakes he made. Where Bruce rejects his chances of happiness and pushes people away, Dick Grayson succeeds in managing to balance a healthy hero and civilian life, of being a crimefighter but allowing himself friends, family, and loved ones. Where Batman can't "turn it off", Grayson found the balance.
And Dick Grayson grew into his own man, stepping out of the shadow of Robin to become Nightwing and reluctantly becoming Batman when the world needed it... and then stepped out of Bruce's shadow to become his own man, his own Batman. Not Bruce, but himself.
When Bruce was "dead", Dick Grayson had to leverage everything he had to restore order to Gotham. But he wasn't Bruce; he wasn't as keen of a detective, he wasn't as experienced, he didn't have the same brute strength. He was more agile and acrobatic, he enjoyed playing mind-games with his opponents more, and, unlike Bruce, he was charming as hell and had a way with people. He leveraged that. No other hero in the DC comics universe probably has the connections and history he has, the deep and unyielding friendship with so many heroes, because Grayson had been a hero since before he was a teenager. When Gotham needed defending, all he had to do was call in those favors, to ask, and everyone - even some villains - respected him enough to do their part.
And when it came time to reform the Justice League, there he was, asking people to their face to join. And his friends responded. "I'm not joining because Batman is asking me to; I'm joining because YOU asked me to."
His dynamic with Damien Wayne as Robin was untouchable and still one of the greatest runs in comic book history. And I hold "The Black Mirror" up as a comic storyline every bit as good as The Long Halloween or The Dark Knight Returns.
For the first time in comics, Batman was no longer in "god mode". He made mistakes. He bled constantly. He screwed up. He was vulnerable. He was insecure. But the weight of the title didn't defeat him; Grayson owned it and made it his own, and the reason it works better for me than it did Terry was because of the history he had with Bruce and the rest of the clan, even their former adversaries. One of my favorite moments was when Harvey Dent figures out there's a new Batman because Grayson SMILES during the fights and enjoys watching thugs flee at the sight of him, something Bruce had stopped allowing himself to enjoy.
Grayon's run was always going to be temporary... but it was a huge thrill, and it was the culmination of a journey that began all the way back in 1940. To see the plucky kid sidekick of Batman grow into the man under the cowl itself still sends shivers up my spine.
Dick Grayson is easily my favorite Batman.