Trying to create a formula to estimate battery life for varied devices
The 6Ah is going to be the battery capacity, probably at 3.7V or so.
So your first number is off by a factor of about 40, if you allow 80% efficiency. So 18 hours-ish.
If they are being honest on battery capacity, which is not at all a sure thing.
The second number is closer, 58-ish W\$\cdot\$h. But they probably don't account for efficiency of the conversion and they may also be &quot;optimistic&quot; on battery capacity so you might get rather less.
The first item also gives the capacity in W\$\cdot\$h at 222W-h, so the claimed ratio is 222/58 or almost 4:1.

My guess on actual performance would be roughly 16-17 hours for the first one to 4-5 hours for the second, at room temperature when new.
Expect to pay a significant penalty in currency and weight to get that higher capacity, and be suspicious if it seems to good to be true.