Actually, you'll want to incorporate BOTH techniques into your riding as they are both valid depending upon conditions. At higher-speeds, you'll want to place body inside of bike to lean it less to have higher cornering power in reserve as well as to prevent scraping pegs, exhausts and handlebars or rolling off edge of tyre.
However, if you are going at slower speeds on more technical course with lots of left-right transitions, moving your body from one side to other of bike requires A LOT of muscle because you're moving body over larger arc than bike itself. This takes longer amount of time and detracts from what actually causes bike to corner...
lean angle of tyre!
Most people think it's steering-angle or countre-steering that causes bike to turn. That's not quite right as those only initiates going from upright to leaning. It's actual lean-angle that causes bike to turn. Once you're leaned over, steering-angle/countre-steering is not relevant as steering is often aimed straight, or even away from corner. What this lean-angle does is make tyres generate
camber-thrust which is actually what causes cornering:
Contact patch of leaned-over tyre is similar to cone with outside edge having larger diameter than inside. Notice that diameter of centre of tire is larger than diameter at edge of tread? This causes leaned-over tyre to carve a curve with larger diameter outside contact-patch edge overtaking and running circles around smaller inside edge. A single tyre leaned over will carve corner
by itself! without any need or help from steering-angle (unicycle).
So larger lean angle, the greater differences in diameter of outside vs. inside edge and more cornering camber-thrust force is generated.
So you have subconsciously picked up on this effect and noticed that bike corners faster and better when leaned over more. At lower speeds, you've noticed that it's much, much easier to get bike from full-upright to full-lean by "counter balancing" or leaning bike more than body. This allows you to do rapid transitions from full-lean on one side to the other because it doesn't require moving your body mass. So you're able to get tyres to full lean-angle quickly to generate more cornering force!
Here's an example of both in use:
Link to original page on YouTube.
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REFERENCES:
https://link.springer.com/chapter/10...-4614-8544-5_3
https://link.springer.com/chapter/10...-030-13062-6_1
https://www.vf750fd.com/blurbs/counter1.html - summary of above