Well, each faction has something different to offer. Each will teach a unique skill, each has a shop with different items, each has a theme you can buy. With all of them, if you manage to claw your way to the top and have more rep with that faction then any other detective, you get something special (no telling allowed). Also, treasure hunts are opened at a specific faction, as long as you have enough rep with them.
For the shops, the prices go down if you have a certain amount of rep with that faction.
As for what they stand for (or represent), you can go read up about them at City Hall.
As for which is most beneficial to get on, that's purely personal choice. Most people eventually get on the good side of all, so they can get whatever is offered (skill, items, whatever).