Well, my Eberron game is set almost entirely in a single city (the PCs have left it once, but only to stop someone else from actually getting INTO the city).
I started the campaign with the PCs on a river barge heading into the city, with just a bit of backstory on how they met each other (they were all hired by the same person, and we riffed off each other to figure out how they had met this contact). And then I introduced them to the docks of the city with the standard "Roll for initiative".
I favour the outsiders approach, since it means a lower learning curve. Saying "alright, you've lived in this city for years" doesn't really work for me; either the players have to invent their contacts for you, or you have to introduce a bunch of NPCs at once and pretend that the PCs have known these guys for years. Plus, whenever you mention something, it has to be followed with an explanation of exactly what that something is; in an "outsider" approach, I can let the players figure things out on their own, and I have much more control over what the PCs know. Things don't snowball as quickly.
The other big plus is that an outsiders game allows for more PC versatility. Players love making weird characters. If I were to set a game in the city of Rome and say "You've all been here your whole life", I could mostly expect Roman characters, or at least foreign characters that have been wholly Romanized. Whereas, if the PCs are outsiders coming into Rome, I can have everything from Provincial Roman Nobles, Druids, Celtic Warriors, Gaul Militiamen, Egyptian Astrologers, Germanic Barbarians, and the "Carthaginian Hordes".
In other words, there are a helluva lot more options open to outsiders over insiders, and that usually works a lot better for an RPG.
Finally, an outsiders game allows the PCs to enter the city fundamentally neutral. This is important for me (especially in my current campaign) because I like detailing multiple power groups and letting the PCs pick which one they favour. For example, in my campaign, the PCs are chummy with the Blood of Vol, simply because they liked the power group (I had originally intended for the Blood to be secondary villains). If the PCs are residents of the city, you sort of expect them to have at least a little connection to one power group or another, which takes away some of the fun of the campaign, in my opinion.
So, yeah, I fully favour the outsiders approach. An insiders approach could work, but I feel it requires much more work, and the work isn't worth the payoff.