The Black Blades
A small organization ranging from a small handful of magi, albeit some of the most powerful short of casting scorcery, you make up part of its membership. Its members typically serve as demon hunters for the most part, though the Black Blades as a whole has little regard for rules and regulations. It's this flaw that usually sets them at odds with the Inquisition, as they tend to "specialize" in inflicting more damage than the monsters that they hunt. It is known that they do recruit from other organizations from time to time, as there are a few former inquisitors that make up their small ranks.
The Holy Inquisition of the Trinity
The oldest demon hunting organization that exists, formed from the three main religions: Christianity, Judaism, and Islam. It traces its roots back to the very first exorcism performed by Jesus Christ in the New Testament, though the organization has changed quite a bit since that modest beginning. For centuries the Holy Inquisition has known about the rifts between the worlds, and has used it to their advantage, developing their own magic. Inquisitors are feared throughout the world for their zealousness, though not all fit that stereotype. Indeed, some might say the Holy Inquisition is just a front for a far more capable organization that lies beneath it. The main conflict that the Inquisitors and the Black Blades have is that the Black Blades not just allow half-demons and magi into their ranks, both of which the Church deems as infernal and something to put down, but also for their lack of rules regarding discretion of their activities.
CORE Security & the Monster Squad
Babylon's finest police force, CORE Security, while not exactly known for "magic wielding gunslingers" and the like, some of them (particularly the higher-ups) do know about the demons and magi that come and go through their city. and thus, have the Monster Squad to patrol the districts with orders to cull any magus or demon they might encounter. They might not use magic, but they are extremely versed in the use of technology to overcome those that do.
While these are the three main heavyweights in the city, there are quite a few smaller groups of demon hunters and magi, either working together to remove a demonic threat, or attacking those who are.