I personally never used any other logistic command station than the mark I.
Higher marks never seemed to bring enough benefits for the knowledge cost. I got to admit though, that the halfing of enemy speed is more than just nice and it basically is what makes these stations an option at all.
I never played against an AI with a lot of teleporting ships though, but that niche seems a little bit too small overall.
When I am thinking about what would make me choose the higher marks, I can't really come up with any new abilities than the ones the station already has.
So what I was thinking is, that higher Mark Logistic stations could Project the speed penalty for enemies to adjacant systems.
This might be an option for one of the higher marks.
The second thing is something I stumbled upon in this thread. The warp gate functionality for logistics also sounds like something that might make me consider an unlock.
Both of those things fit perfectly in the theme of mobility and control.
So I would put it together to:
Mark II: Provide warpgate functionality with reduced paralysis compared to the actual warp gates. (This might need a major pathfinding overhaul... not sure about that)
Mark III: Project Speed reduction to adjacant Systems.
Alternatively to providing full warpgate functionality, the logistic station may also provide reduced paralysis for warp gates in the same system, thus still going for enhanced mobility in a way.
No idea about the military ones though. I use them in borderworlds, also higher marks of them. They do a pretty good job there in holding the line, if the defense is laid out to make maximum use of their abilities.
As a sidenote:
Reducing the amount of buildable command stations of higher marks and boosting their stats and benefits alltogether as a tradeoff felt to me like something that would encourage a lot more strategic choices. Right now I rarely am able to place all higher mark command stations, even when just unlocking one branch of them. And after all... it's about strategic choices, that is why I love this game