I usually just spam mines for that sweet, sweet 1 in 10000 chance of hitting silver... If you work enough mines per turn, its actually more likely than you think... if you can work 100 mines over 100 turns, you'll find that silver, more likely than not.
But seriously, let's think this through:
The real question is this: let's say a city reaches happy cap or runs out of things to work and so it doesn't need as much food as it has. What's better:
(A) Turn a farm into a workshop
(B) Turn a windmill into a mine.
So you have several stages in the game & strategies to consider:
After machinery but before anything else relevant.
At this point in the game, workshops are trash, so why build a windmill if you can just get your food from farms instead? No reason to build a windmill for this stage in the game unless you're desperate for workable squares in a food-starved city.
After Guilds, Chemistry, and Replaceable parts, but before biology and railroad.
This is when windmills really shine. Your workshops are now doing real work, so they're your source of hammers, which means you need to make up the food from somewhere. A windmill now has only -1 hammer compared to a mine, while giving +1 food. Better ratio than using a farm over a workshop, while giving more commerce to boot.
Makes sense to run workshops/windmills at this stage in the game. So if your game plan is to rush cavs or riflemen and then stop teching for a while, then just windmill everything you see.
After Biology and Railroad
Now it's back to farms/mines having the advantage.. Turning a farm into a workshop now gives +3 hammers for -3 food, which is not a good ratio, but turning a windmill into a mine gives +2 hammers for -1 food and -1 commerce. So the farm/mine combo is back to being better.
If you're using mining inc, mines are especially good since the bonus resources are so much more valuable now.
With State Property & Caste System Economy.
On one hand, you probably want to run all workshops on all non-riverside flatlands, so if you do that and still need food, its probably better to lose a mine to a windmill than a workshop to a farm.
On the other hand, you probably don't need a lot of extra food with all the awesome workshops and watermills.
So you're probably running mostly mines and workshops, with the occasional windmill in a food deprived city.
After Electricity
Windmills are probably worth considering again, for the bonus commerce, but I still think mines are better in most cases, since hammers >> commerce in any city without a lot of +sceince mods. Its also probably too late in the game for the free resource pops as big of a factor. Maybe you've had time to build more science buildings to get the mods for extra commerce... if so, go ahead and windmill over some mines.
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But I think that the chance to pop resources is a non-negligible bonus... it happens even if you turn off events... let's say that you can improve your overall commerce output of your empire by 100 points per turn with the extra happiness from a luxury resource, and there are about 100 turns left in the game, you're missing 2 of silver/gems/gold... each mine then has a 2 in 10000 chance per turn of giving you 10000 commerce over the course of the game... although its backloaded, that's worth more IMO than the 1 commerce/turn from the windmill. Odds get even better if you're running mining inc since you'd be happy to find even non-luxury resources. I feel like if I spam mines everywhere, I usually get about 1 free resource pop per game...
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anyway, slavery starts to get really bad once city sizes increase and food costs to grow increase and almost every tile is producing large yields. Why whip when you can just build normally and have it done in a couple of turns? I don't think its optimal to run slavery late game.
