Advent starbase: Tradeport that is about as effective as two normal tradeports, 30% extra allegiance (equals 30% stronger resource and planet income), extremely strong temple of communion. Takes up 6 starbase slots, frees up 20 logistic slots (if all abilities were maxed out) on backwards planets. Leaves open two slots (1 can be used for aux gov if needed).
TEC starbase: Tradeport as effective as 3.5 to 4 normal tradeports (on step 2), frigate factory that builds 2 times/3.5 times as fast as a normal one. Takes up 4 starbase slots, frees up 28 logistic slots. Leaves 4 slots on the SB.
Vasari Starbase: Phase stabilizer, tradeport roughly as effective as 2 normal ones, colony pods are immune to planetary bombardment. Takes up 4 starbase slots, frees up... 8 logistic and 8 tactical slots I think. The weakest economic effect of all starbases, but the freed up tacticals can be very useful.
The Vasari starbase is the least useful to use on backwards planets right now, but the immunity of their colony pods from all sorts of eco debuffs can be valuable in certain situations.
Edit: I don't have the exact numbers in my head right now, but I think that is bout the gist of it.
Right now I play versus AI a lot more, but in diplomacy the rate is about... 50/50 I guess. I'm more of a defensive player so I'm more prone to have starbases out early than someone who tries to steamroll players early on with fleet, but I always try to balance increasing my fleet size and securing my lines.