If you have a hex with a hill and forest, you get one food and 2 production. If I then but a lumbermill on it, the production get's increased by 2, but if I remove the forest and then build a mine on it the production also get's increased by 2. (First you lose one but then get 3 production) Q: Why should I ever build a Lumbermill, when I have the same outcome with a mine but still get the production-bonus from cutting down the forest?
To clearify: You get more than 50 production for cutting down the forest and you just need one charge of you builder.
EDIT: I didn't express myself fully, the only Condition I want to be met is, that it's forst + hill. But if there are other boni I didn't notice (e.g. Tech that increases lumbermill production) please hint me on them.