I doubt it is the size of the tip so much as it is the composition of the material being cut.
What I usually do is light the torch with just the fuel side on. Then I slowly add the oxygen until the flame loses it's feather and is just a circle of pretty little blue green cones, no feathers on any of them puppys.
The way it's been explained to me is the flame melts a spot and then the oxygen under pressure uses the melted materials to burn through.
If the surface melts and when you hit the oxygen it just moves around sorta like brass when brazing then you're dealing with cast iron and the only way to cut it with a torch is to just melt it through. But if when you hit the oxygen it sends sparks everywhere, especially you hair and inside your ear, then I try to just keep working it until it burns on through.
I once worked with a weldor who was an ace with a cutting torch. He couldn't do much well but he could walk and talk and do a dance cutting. He'd found his calling and he did enjoy it. He told me about freehanding cuts through six inch plate. He explained that cutting through stuff that thick involved not such a killer big tip but having plenty of oxygen flow. So they had a manifold of tanks set up and a large hose from the manifold to the torch just to keep the oxygen flowing at a rate that would push the molten metal right on through. He would also drive you up a wall cleaning the tips. He was heck on tips. He'd wear them out just cleaning them.
We use to laugh about him being a one trick pony. But looking back I can see where maybe the reason he could cut so well was he understood that clean tips were like having good shoes when doing that one dance like no one else could.