Oh, and one final thing to consider. Raw ability checks are supposed to be few and far between. That's why you have skills.
Athletics should be used for most Strength-based activities.
Acrobatics should be used for most Dexterity-based activities involving flipping, balance, etc.
Arcana should be used for most Intelligence checks in the field of magic.
Religion should be used for most Intelligence checks in the field of deities, cults, etc.
Medicine should be used for most Intelligence checks in the field of potions, cures, bandaging, etc.
You would RARELY make a raw Intelligence roll. Likewise, most of the time you don't make a raw Strength check. You usually use the skills that go with them.
So, the proficient, intelligent character might get a +5 to their roll as opposed to the unproficient, unintelligent character who gets a -1.
In your scenario with the Strength 8 versus the Strength 20, the one with Strength 20 is also probably proficient in Athletics and would thus gain not only the +5 for raw Strength but also an additional +2 or +3 at lower levels for a +7 or +8 which is then a considerable difference from the person who gets a -1.
That is why grapple and shove are Athletics rolls, not raw Strength. Likewise, busting a door down should probably be more of an Athletics roll than a raw Strength roll.
