Amp hours and longevity may not be related. Perhaps it depends a bit on how deep of discharge cycles (40% discharge cycle sounds good).

However, another way to look at it. Say you have you 20 mile commute.

With the first battery, you drain it 80%, with a 20% reserve capacity.

Over time, that reserve capacity will decrease, so your 20 mile commute will eventually start draining the battery 100%. Any more, and you'll be pedalling.

With the more expensive battery, you drain it 40%, and have 60% reserve capacity. In theory, it will take longer to reach that magical 100% drained and 0% reserve capacity point.

Another rating is to look at the various discharge rates. The maximum discharge rate is typically close to 1C. So, your cheaper battery will discharge at about 10A (about 480w), and the more expensive at about 20A (about 960w).

And, like above, the discharge rate will decrease with both age, and battery charge. So, your more expensive battery will give you more power, especially as the battery ages, and is drained.

Will your route ever vary? 30 miles? 40 miles?

Anyway, personally, I tend to like to choose higher capacity batteries for my needs (not bicycle power).