@mainiac
I disagree with your analysis of the ministries' value.
The Fleet has indeed the easiest to use and posesses strongest units, but it's very situational. That is, you have to be at war to make good use of it. Sure, you can bomb some rebels from the orbit, but that's a minor thing.
It's other stregth lies in the "fleet in being" effect on other players. That is, it dissuades aggression against the holder of the ministry, but it's practically irrelevant in the early game, and from the mid-game peak onward it's got an ever diminshing value.
I should also mention that even devoid of its ships, it still posesses a large garrison on Byzantium, with less-advanced, but significantly more numerous troops than the Eye, and backed by the infrastructure to produce and, perhaps more importantly, transport more. So it's not like it ever becomes an empty ministry.
Still, for the better part of the game, when most players are not at war, I'd much prefer the Eye. Mainiac did not mention the main asset of the ministry, which is a number of spies and easy way to transport them across the galaxy.
The knowledge of other player's actual strengths and weaknesses(as opposed to the useless score graphs) is invaluable to planning one's strategy.
The many spies and lander transports allow for rapid exploration, and facilitate pinpointing and conquest of ruins and valuable land.
These are all immediate gains, with large impact on the way you conduct your expansion and diplomacy, while the Fleet spends most of the time just sitting there, doing not much at all.
Stigmata, apart from being too much of an additional micromanagement for my taste, similarly allows for immediate gain by clearing the ruins on Symbiot worlds.
In most games their tiny fleet is almost certainly destroyed by the symbiots, but in this one it is intact, allowing it to gain access to ruins on other worlds, and perform a similar to the Fleet's role of aggression deterrent, albeit unlike the fleet, it's mostly about the land units.
Of course, the ruins are a scarce and non-renewable resource, so the potential gains are limited.
There's also the possibility of the ministry controller gaining access to the resources in Symbiot worlds, but this is very much dependent on how close to the Stigmata a given house is located.
What I'm saying is far from trying to rank the ministries. In my opinion the value of each depends strongly on the circumstances one finds himself in, but it so happens that the circumstances for usefulness for the Fleet are the rarest, even if it does pack the strongest punch.