As someone said before, which corporation to pick is situational. Often it depends on having the right GP, technology, and resources. Empire size and geo-politics (war) may be even bigger factors. For example:
Currently, I'm playing a game where I have a sprawling empire, with 15-20 cities on my main continent, which I own entirely, and multiple island holdings - recently settled or conquered - each with 3-4 cities. I have over 2x the score of the nearest AI, and a modest tech lead - actually a large tech lead over some of them (infantry vs. LB). I just conquered a small, backwards AI, so I have a fairly powerful army, which could easily roll over other backwards AIs. That's just what I'm going to do, in addition to settling more islands, since my tech rate is holding up well at 70-80%.
Should I use corporations?
Certainly I would get a large boost in food or hammers, since I have a pretty large land holding. In this case I would lean towards something like Mining Inc., since I want to get newly acquired cities up and running economically ASAP. Food is not as good for this, because I don't want to run Slavery - someone else is running Emancipation already, and I need Emancipation for my cottage economy. This is not to say food isn't useful though, since it would be very helpful in letting me build more hammer and commerce improvements. In my situation, having a culture-producing corp would help pop borders and help border cities if I wanted to vassalize, but it's just a nice-to-have.
But there's an opportunity cost. I'm currently running state property, to eliminate city maintenance costs due to distance. The food is nice too. And my empire will only get bigger. My leader is organized, but I'm sure state property is still helping. I'd also have spend hammers on execs. However, my guess is that if the corporation is spread to enough cities, it surpasses state property economically. Does anyone have any idea when this is?
Tempting as they are, I think corporations might not be worth it if I can maintain my current military advantage to win. I have the Mausoleum too, so maybe I should just use GPs for golden ages. If I were to go for a space victory though, I'd definitely get corporations.