I do like the intent of the topic cretor, which is (if I'm reading correctly) to make the player choose between multiple city types to prevent the player from spamming an identical "optimal city" build over and over.
It would kind of be like in Medieval 2 Total War. Every settlement could either be a "castle" which produced the best troops and was difficult to seige, or a "city" which didn't train as good units but was an economic center. You needed to find the right balance with mostly citys, but with enough castles spread around to be able to defend your borders.
Now, the TC's idea isn't nearly as cut and dry as that, but the concept of having cities that have strengths and weakneses is still there. However, I not sure I agree that it should be the central "castle" of a city that determines that.
I think galciv2 worked fairly well with it's capitals. I would usually have one planet full of banks and an economic capital, a research planet with only research centers and the research capital, etc. It led to my core planets being highly specialized and valuable, and my border planets to be a bit more generic. If they could expand on that somehow, it would work to add diversity to cities.
Perhaps you could even have a generic bonus as well. eg. One barracks in a city produces troops at 100% speed, two produce troops at 205% speed, three at 310% speed. I would very much like, for the sake of feel, visual signals for this as well. Many forges in a town would lead to a cloud of smog above the city, lots of magic labs would cause the city to glow faintly, and runes to float about, zooming in on a military city would treat you to marching drums and seeing tiny soldiers drilling.