Warning: Contains spoilers for Peacemaker episode 5.
Despite the nature of Peacemaker as a character, the avoid the Batman problem.
In recent years, Batman has increasingly been criticized for the fact that his superpower is ultimately having a lot of money and no consequences. In his move against organized crime, Batman functions in a similar way to a police officer but with no restrictions on hurting people or breaching their privacy. Many have now pointed out that he could achieve greater social change through the use of his fortune (an element that DC has tried to combat with the Wayne Foundation), but as he pursues his nighttime activities he creates his own authority and has no check or balances on his actions.
The Peacemaker TV series cleverly manages to avoid this problem that plagues Batman and other vigilante stories. Because Peacemaker is forced into service by the ARGUS team, he is able to serve outside of the usual law without acting free of consequences and oversight. However, Peacemaker also avoids becoming a police show by having the agency that he gains authority from having to work around a compromised government and compromised police force to try and actually serve the people. This is helped by the fact that Peacemaker shows hesitation about killing people he is not sure are possessed by aliens.
There are several hints that suggest that the Peacemaker TV show takes place in an alternate timeline within the DCEU. In this timeline, according to White Dragon’s neighbor (Mel Tuck) Batman doesn’t kill. However, within the Zack Snyder-led films in the DCEU, Batman explicitly kills multiple people, including low-level goons. This means that Peacemaker’s distance from Batman’s wanton vigilante role is all the more important for the wider DCEU.
The distinction between Peacemaker and a vigilante who kills people without hesitation, remorse, or oversight is of course emphasized in the Peacemaker TV series by the presence of Vigilante (Freddie Stroma). If Vigilante is to be taken at his word, then he uses lethal force against people who commit even minor crimes like graffiti or doing illegal drugs. The inclusion of this extreme version of what is essentially the Zack Snyder Batman vigilante problem makes it seem likely that James Gunn made a conscious decision to avoid that issue with Peacemaker in the Peacemaker TV series. Regardless of whether or not this was a deliberate ploy, however, it's clear that Peacemaker's main protagonist is arguably more complex than the questionably heroic modern depiction of Batman.
Peacemaker releases new episodes Thursdays on HBO.