WARNING: The following contains SPOILERS for Batwoman, season 1, episode 12, "Take Your Choice."
The latest episode of Batwoman has shown that the Crows, the private security firm run by Jacob Kane, are somehow more incompetent than the Gotham City Police Department. This is something of an accomplishment, given the GCPD reputation for corruption and general stupidity.
Crows Security was founded after Batman disappeared from Gotham City in 2015. Made up of Navy SEALS and Green Berets who had left active military service to enter the private sector, the Crows were theoretically meant to offer Gotham City a team of professionals who would be able to protect the city in ways the GCPD could not in Batman's absence. In practice, however, the Crows were mercenaries whose services were affordable only to the wealthy elites running Gotham City. This resulted in crime increasing in the worst parts of Gotham and the GCPD becoming even more overburdened as funds that might have been donated to the police were instead used to hire the Crows and enrich Jacob Kane and his wife, weapons magnate Catherine Hamilton.
It speaks to how bad the Crows are at their job that one highly-trained person in a bat costume could do their job more effectively. Jacob Kane was aware of this and made capturing Batwoman as much of a priority for the Crows as bringing Alice and her Wonderland Gang to justice when she first appeared, as much out of fear of his soldiers being shown up as a belief against vigilante justice. Or at least freely-offered vigilante justice that didn't profit him. "Take Your Choice" firmly established the ineptitude of the Crows, as they launched a city-wide manhunt for Alice after she escaped from their custody. Their investigative technique left much to be desired, seemingly consisting of sending SWAT teams into random abandoned buildings and harassing the homeless, while setting up checkpoints along every major street in Gotham City to search every car in the area Alice was last seen.
In defiance of this impressive display of military might, Alice was easily able to kill one lone Crow and steal his uniform, and then use it to infiltrate the hospital where her right-hand man, Mouse, was being treated following a battle with Kate Kane (outside of her Batwoman costume). Despite Mouse being under 24-hour surveillance by the Crows, Alice was easily able to waltz past the Crow watching Mouse's room without having her badge or any other credentials checked and making no effort to hide her face beyond wearing a Crows ball-cap. Somehow, the highly-trained security professional failed to recognize the face of the woman he was meant to be watching out for and thought nothing was strange about one lone Crow going into Mouse's room, claiming she had "orders to transport the inmate," and then not actually taking the inmate with her when she left. This ignores how the Crows are meant to be a tight-knit group where everyone knows everyone else, so the odds of there being a new recruit he didn't recognize working alone were slim to none.
The general denseness of the Crows is also on display in the climax of the episode, where Alice is finally captured by Kate Kane's stepsister, Mary Hamilton; a medical student with no combat training. Left handcuffed to a hospital bed, Alice is still able to get a hold of a phone and puts in a call to Crows Security, telling them that Alice is hiding out inside of Wayne Tower. This results in a team of 50 Crow soldiers, 10 trucks, and one helicopter swarming around Kate Kane's base of operations, with no one having questioned where the tip came from or the likelihood of a prank call from Alice herself targeting a property managed by the Kane family against whom she holds a grudge. With fools like these charged with protecting Gotham City, it's no wonder the common folk prefer Batwoman to the Crows.