Honestly, I don't notice a difference between any of the three. If you've visited my cleaning thread sticky, you know I'm a cleaning nut. I used to be more OCD than I am now.
Cleaning Barrel = dry patch, wet patch, dwell time, wet patch, wet brush, dry patches, end with a lubed patch.
Cleaning Chamber = Chamber brush, swab out.
It's the same pattern, same amount of patches, no matter what. What makes a difference in cleaning is a Nickel Boron treated Bolt Carrier Group. It just wipes clean. If you have a standard phosphate coated BCG, then the CAT M4 tool makes cleaning easy.
The gas tube keeps itself clean. The hot gasses burn off any carbon deposits.