Anytime your saw is throwing dust, it is almost certainly dull. Really sharp saws throw nice sized chips regardless of the hardness of the wood.
As to why dust is more prevalent on bigger cuts? That is a simple function of downpressure and how much area said pressure is applied to. When a saw cuts a small branch, all the down pressure is applied to only a few cutters, so each cutter engages the wood with a full depth pass, throwing chips all the way.
Change that scenario to a bar engaging 20 inches of wood. Now you have 20 or more cutters supporting the same down pressure applied by the saw operator. That means less pressure-per-tooth, and consequently less penetration into the wood. That means smaller chips and slower cutting (per tooth).
Now take that same situation and dull each of the teeth. The operator cannot increase the pressure too much, as the dull teeth will just stall the chain in the cut, the cutters barely scratch the wood without a lot of additional pressure. So now you are getting sawdust!
A badly dulled saw won't even make sawdust on the full bar width, but you can take the tip of the bar and run it back and forth across the length of the cut to still get the job done. Not the best plan, but it works in a pinch.