Pragmatism could be a factor, as the winning side will receive a card that you can use to gain favor from that side.Some people want criminals to win so they can trade favors for tribute in Labyrinth.
Another factor is likely that Constables, at least in London, are extremely corrupt, making it difficult to argue that constables represent even order and adhere to laws that are enforced (albeit selectively).In addition, it’s nigh-impossible to play a character without breaking some laws (especially on the shadowy path), as many plots will involve you at least breaking in to some place, and some items can be obtained only via unlawful activities (or at least that was the case in the past). Mind you, constables have their own institution dedicated to censorship and cracking down on freedom of expression.
Naturally, criminals are a morally worse faction than constables when they are not corrupt and do not enforce some draconian laws. But I suspect those who support revolutionaries will lean toward criminals as well due to the ties of constables to masters.