I finally got around to running the break even analysis of advanced farms and mines, and found a highly discouraging result. If you upgrade one advanced farm and one advanced mine to level 10, it will take 213 (7 months) days to recover the food cost and 456 days (15 months) to recover the iron costs from upgrading the buildings.
In my opionion, this lengthy payoff period makes these upgrades a very low priority. Given the plethora of other uses for food and iron, I highly recommend that players NOT upgrade farms and mines unless they have no other way to spend their resources. Leveling heroes, troops, and upgrading the Hunter’s Lodge for 5* battle items will have a quicker and more impactful payoff. Upgrading advanced farms and mines should be the lowest priority when you have no other good uses for food and iron.
Addendum: Since many players are strapped for food but have ample iron, it may be worthwhile to upgrade a farm but not a mine. The advanced farm pays for itself in a long but not unreasonable time, whereas the advanced mine takes a ludicrous amount of time to pay for itself.