I'm a relative nobody, but for the last year or so I was only been able to play Injustice with
@Pnut exclusively. It always boiled down to Batman vs Sinestro, and this is my take on the MU:
Batman can neutralize some of Sinestro's main tools. B12 being punishable by bats is dumb, Batman's small hitbox dodges Fear Blast and often forces the Sinestro to use a bar of meter to not be punished at mid-range with trait, and good Batman players will only be jumping at a range where Sinestro's D2 is unreliable and therefore not worth the risk. Combined with the fact that Batman's high combo potential and excellent mobility, it can be argued to be 6-4 Batman's favor.
Sinestro still has tools that he can fight back with. For example, off a knockdown Sinestro can do a free left/right vortex on Batman. Should Batman choose to avoid this situation with his only invincible wakeup of slide, Sinestro gets a free punish with B1, which leads back into the vortex. Sinestro also heavily outfootsies Batman when he doesn't have bats. True, Batman gets trait for free and good players will insure that there is always 1 bat available in neutral. But one trade, one errant Fear Blast hit, one good use of Sinestro B1 means trait goes away. Batman cannot effectively approach Sinestro without bats, and he cannot check Sinestro's zoning, footsies or trait charge.
Everyone must also remember that we are playing Injustice here too, where interacables are a big deal. Most stages favor power characters, and Sinestro with trait can guarantee interactables. When Batman has to eat an unescapable TV to the face, he gets pushed back, loses bats and Sinestro is at a huge advantage in the neutral. Even the interactables that can be dodged with a double jump forces Batman backwards, and again leaves Sinestro at a huge advantage. Combined with good/great interactables located in the corner of every stage, even patient Batman players that walk their opponents to the end of the screen are in a bad position.
Personally, I have to call it at 5-5. Batman relies entirely on bats for this matchup, and they are extremely good. The strength of interactables as a whole give Sinestro enough firepower to fight back.
TL; DR: Bats + small hitbox = B1 + interactables