If someone invents dirt-cheap power and replication, and if everyone could behave (or be medicated to behave), we get the ideal world of Star Trek (or Larry Niven's Known Space). Everyone can be comfortable, nobody needs to steal, any violent tendencies are obviously mental illness that needs "curing".
If we consider historical example, we get subsistence-level colonies like Star Wars (except for the Jedi, which are fantasy). Or, more realistically, big modern cities in the center of things and subsistence-level colonies like Firefly, which is itself a tramp steamer just like the "African Queen" in space.
It also depends how long it takes to get anywhere. If travel takes months or years, shipping is only worthwhile for durables like minerals and manufactured goods; and each colony has to become more independently technological. But if shipping is weeks, and perishables can be frozen like New Zealand lamb getting to the rest of the world, then colonies can remain more "backwards" farming suppliers.