A lighter gun shooting the same payload as a heavier gun cannot deliver less recoil. Physics.
A lighter gun shooting the same payload but that fits better than the heavier gun may seem to deliver less recoil. But it doesn't. Physics
A lighter gun shooting a lighter payload will, at some point as the payload diminishes, deliver less recoil. The shotgun recoil calculator referred to above can provide the exact load at which this happens.
These are not matters about which one can have a valid opinion. They are facts, immutable and constant: A 1 oz load from a 7.5 lbs 12 ga will deliver less recoil than a 1oz load from a 6.5 lbs 20 ga (at roughly the same fps) every single time each is fired, every day, for every body. It never, ever changes. One may have an opinion about how one feels versus the other. But opinions are like...belly buttons.