I personally think the Lumbermill nets you a greater hammer/food ratio. A mine cost 2 food to work and delivers 3 hammers. For the same 2 food you can work 2 lumbermill (since a forest always produce 1 food, so effectively, it cost you a netto 1 food to work) and delivers 4 hammers total. In late game you get +1 hammer on lumbermill, so 6 hammers total, twice the mine output!