Agree with Faulty Logic on the usefulness of various CS. Note that Logistics stations are +Speed so they benefit slower units more than faster units.
At the Mark I level, I think all three CS have uses. But at the Mark II and III levels, at least in higher difficulty games, you just don't capture enough systems to need that many CS. I'd say the best change they could receive would be cap reductions with corresponding stat buffs. Caps of 4 of Mark II, and 2 for Mark III would probably be a better option.
As for each individual CS type at the Mark II+ level:
Economic: These break down to a simple K-cost per increased M+C/sec and are directly comparable to Harvester upgrades. At current caps, Harvester III works out to be better than Eco CS upgrades in basically all cases, and it doesn't have the opportunity cost of not being able to put a Military or Logistics CS in a system. Keeping the total cap M+C output the same for Eco CS upgrades but lower the caps to 4 and 2 would actually make Eco CS slightly better than Harvesters for small empires. I still feel they might be a little weak, but at least they'd be usable. Maybe a Construction Bonus to all Build Queues in the system would be good.
Military: Oddly this is really a stalling CS, not a combat one. I think I'd really prefer if Translocation shots went to a forth CS type (maybe even move to the Warp Jammer CS?) and the Miltary CS got a more meaningful combat attack like long range missiles. Then Mark II and III could expand its combat ability more. So Mark II might get AOE missiles (aka, Grenade Launchers) and Mark III Engine Damage added (remember, the cap would be 2). Mark II and III benefits could be reversed.
Logistics: The upgrades here are a little spotty. I'd inclined to think at Mark II giving it a +x% engine damage boost (like attack boost, but only applies to engine damage) might be interesting and in theme. Mark III's anti-teleport is nice, but maybe another defensive like Absorb EMP or even prevents enemy tractor beams from working.
Warp Jamming: If this got the Translocation shots, it would fit perfectly with its use as a stalling/satellite CS.