No, mines are far superior.
Except when they're not.
Hills are great for production, there's no need to waste that.
Only in some combinations of eras/technologies/civics. For example, with caste system, state property, and chemistry, the best possible production city without any special bonuses is 18 flat grassland and 2 flat plains. (use 20 workshops)
Windmills/watermills are
really good improvements for maximizing production when they get their bonuses at replaceable parts, because farms are terrible at that point in the game: farms give 1

while windmills/watermills/mines/forest+lumbermill all give either 1

1

or 2

.
The relevant thing to look at is the opportunity cost of food versus production -- you need to select your improvements to maximize the number of hammers you get per food you give up. At replaceable parts, we have:
Giving up a farm for a watermill = -1

+2

Giving up a windmill for a mine = -1

+1

(+ commerce)
From which we see that watermills are preferable to mines if you want to maximize production. Accordingly, we replace our farms with watermills as much as we can, and replace our mines with windmills to compensate.
If we happen to have caste system and chemistry, we also have:
Giving up a farm for a workshop = -2

+4
After getting biology, things equalize out in terms of production, but windmills/watermills remain slightly superior because of their commerce bonus. Mines only become desirable again if you are not running state property and you have railroads. (Or just can't find any other efficient way to spend your food)