As always, first of all a summarized comparison:
For medium and short range, if Comic version can't use his Barret then he is in a bad position compared with his "rival". Although both of them are equipped with the 9 mm Twin Cannons, Arkham City version can combine them with his Night Vision, being able to ignore 1 Ping! for being Shooter in addition to the possibility of increasing the difficult of the rest of them in 1 point for Expert Marksman (1 SC). If he doesn't move he can deal up to 6 blood damage, and if he does he can still shot with ROF 2 thanks to his Rapid Fire (1 SC). Meanwhile, Comic version only has in advantage his +1 to impact with ranged attacks for being Ranged Master, although if he can use his Barret, he is still much better than Arkam City.
But this section can't be closed without talking about the big handicap of Comic version, and it is his Obssessive which forces him to focus the same target until he puts him KO (or death). This inconvenient can be easily solved by killing an easy target with Endurance 4 (and Defense 2-3 because for him there are still impact rolls to 2+), although a 1 either impact or damage can become him useless if the enemy puts that target inside a sewer. Most common will be to harass the enemy Boss mainly for his Assassin/3 that will grant him 3 VP more if he kills him, and useful also for dealing against annoying characters such as Free Agents, Sidekicks...
Another subtle difference among them is their quantity of ammo, Comic version has 5 clips in total: 3 for the Barret and 2 for his Twin Cannons, while Arkham City version can shot one time less with 4 clips for his Twin Cannons.
CLOSE COMBAT ATTACK
If he is engaged in close combat (or any enemy is within 5 cm of him) he can still use his 9 mm Twin Cannons thanks to be Light, and once again Arkham City version is dangerous for his Rapid Fire, without forgetting that even in close combat distance not everybody can avoid shots, only characters with Dodge. Once again, the good point of Comic version is his +1 to impact, but only with 1 dice.