I run bore snakes after every range trip and/or routine maintenance. They work pretty well (as noted by shining a light down the barrel). My technique is spray down the barrel/chamber with solvent, let it sit for a few minutes while i clean other parts. Clean out the chamber area (especially AR). Spray more solvent and a little oil on the bore snake and run it through a few times. I suppose it depends on the brand of bore-snake, but the ones I have start with some cloth (solvent), then some bristles, then more cloth (oil), then a big hunk of cloth (serves as patches).
It’s really fast and low-effort.
If you have a lot of copper build-up, or some serious fouling then maybe go the old-school way, but most of the time a bore-snake is plenty