I have now played large campaigns in each race.
After playing the Vasari, and then playing Advent and TEC, my first reaction was that of many here on the forum: Why don't TEC and Advent starbases move?
When I played Advent I tried to utilize the Advent culture abilies of the Starbases to maximize my culture. I was disapointed that, even though I had several starbases with Evangilization Nodes maxed out, and they virtually sourounded the enemy planet, the enemy planet did not evacuate. It seemed proximity to home planet was enough to keep hostile culture at bay. Point being, for three starbases bordering the planet and three Evangilization Nodes on each one, and culture tech tree maxed out, Deliverance Engines shooting every which-way, I would think that would be enough to smother an adjacent planet. The Antimatter upgrades don't seem to be as powerful as they should be. Meteoroid Control doesn't seem balanced with Phase Stabiliser Nodes of the Vasari or Security Overide Protocol of the TEC. Mass Disorientation seems to work OK... I've seen it used againts me, anyway.
The only use I had for TEC Starbases was Safty Override Protocol. It is a singularily brutal attack, and I completed any number of "Destroy Ships" missions by using it. The one I found least useful was Auxilary Government (which all races get). All the others have their own, case-by-case usefulness. But as TEC, I usually put two points in Safety Override, one in Structural Integrity, and wait for an ememy fleet to attack it. Also, I haven't been able to confirm, do Docking Booms provide antimater to ships like the Advent Antimatter Recharger? I haven't confirmed this ability. It would be more useful if it provided Antimatter to structures as well, since odds are, if you left a Starbase there, you don't have your fleet there too.
The Vasari Starbases seem overpowered with their colony pods and their movement ability.
The starbases are nice: they allow trade ship routes to span uncolonizable areas, sometimes build more fleet (although this should sync with any construction facilities on the planet - it's anoying to have multiple waypoints set, one for the Starbase and one for the planet, as is the case with TEC), and provide short and long range attacks of dubious usefulness.
For the record, I don't think any race needs phase stabilizers built into the base. I don't think TEC and Advent Starbases should even, necessarily, move. But what they do need (at least TEC and Advent) is a weapon that is capable of taking out a ship. I shouldn't be able to destroy a maxed out 15000 hp starbase and loose nothing.