Thanks for the answer.
There's a theory that was debated on the vanilla boards when Civ4 first came out that might be useful for consideration. It's based on an analysis of various kinds of "converting this to that" options in the game mechanics, from whipping to tile improvement options to specialists. In short, the comparison is every bit as subject to "if/then" conditions than the eternal CE/FE debates. I don't believe it as a literal conversion that provides hard numbers, but the concept behind seems pretty solid.
1 food = 2 hammers = 4 commerce
Again, I'm NOT making the case that this is literally true, just that the hierarchy holds in general terms and it can be used for a rough comparison of the relative value. Whether you think it's 1:2:4 or 1:1.5:2.5 or whatever, Food>Hammers>Commerce and that makes it possible to get a rough ranking of the improvements.
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Windmill is the best. The more you weight food, the better it is in comparison to anything else, though Farms/Sanitation gain.
Farms with Sanitation are next, depending on the food weighting. In no case would they be worse than Mines and Towns
Farms without Sanitation, Mines and Towns are next. If you drop the food weighting farms might fall below. However, they are from a starting tech while the others take more time to get up. Mines take a lot longer than Farms to improve via tech, and Towns have time and plunder weakness. Even if you want to go with Mines or Towns, you'll probably still want to farm first, then switch tiles/improvements.
Workshops and Lumbermills are the bottom. The more you weight food, the worse Workshops are.
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Now, obviously, all of that is going to be extremely situation dependent. If you have 2 forests in a grassland city, those hammers from a Lumbermill will be extremely important, well in excess of just the raw numbers, and having no tree option means that Workshops are much more important. Also, there are limits on both the efficiency and capacity to convert among the types of production so even specialized cities will likely need a bit of each, e.g. only so much food is useful in most cities as even whipping and feeding will eventually bump happy limits.
However, overall, Lumbermills are mediocre and workshops just plain suck until late enough in the game that you can likely have Windmill techs anyway. They are basically strictly specialty application where the other options don't exist due to terrain. More importantly, with the Workshop improvement techs coming quite late, Lumbermills are better in that niche for a long time as long as the option exists. In Vanilla, they eventually come into their own with State Property because they get +1 food but that's not present in FFH. Without it, the primary use for Workshops is in an extremely food-rich city without hills to mine. Personally, I can't imagine using them in any other situation.
I would recommend a boost for Workshops, but I think that if they were boosted, then that food-rich city with lots of Workshops would be better than any production city in the game with the possible exception of lots of Arete mines.
As noted, Windmills are the best overall, as long as they are an option. As drawbacks, though, they are quite late in techs and they are all-rounders so their application is limited for highly specialized cities. I think they are probably just fine.
Farms, Mines, and Towns are mostly balanced and in any case are complete distinct in their roles so they are fine.