This is a complex one and will bring up lots of different answers from different people.
I've tried most methods including VFG rods and paste, to home made wires and all the currently available pull through's, but usually find you can get virtually everything out and get clean barrels after either four or five for a regularly cleaned barrel, to 12 or 15 and sometimes more pull through's, with an uncleaned barrel, using my home made nylon coated wire and soaked cloth, depending how dirty the barrel is.
I find the felt shoot though's ok as a final dry wiper only and dont take much dirt out like a cloth on a wire with napier oil or similar. You must have some kind of cleaner on or you are just dragging over the dirt and grunge.
I think also that even when clean you sometimes get a tiny amount of rifling lines.
I probably clean my barrels every couple of tins on average, or when the grouping opens up with a known pellet.
If you leave it more than this you will take more time to clean it, and a shoot through pellet will never get a barrel completely clean, well maybe if you put a full box through it.
I am in the process of buying a Steyr so I will have to get some industrial cleaner and a brass brush by the sound of their barrel reputaton.