Mass Disorient and Meteor Storm are pretty powerful abilities.

Disorient shuts down engines for a pretty long time and it shuts down maneuvering as well, meaning affected ships just spin around out of control and mostly can't even fire because weapons/abilities require facing the target.

Meteor Storm targets a ship and throws down meteors on all ships nearby (with "nearby" being enough to hit the majority of the enemy fleet, if not all of it) for 500 damage. It should be 750 with rank 2 of the ability, but it seems to do 500 still for now. Even then, its cooldown is short enough that 3 500-damage meteors can usually take out light frigates and long range frigates in a fleet, unless they come with a lot of AoE repair.

on the civilian side of things Advent get the culture upgrades and the alliegance boost upgrade as unique improvements. the alliegance boost can actually result in a large income bonus if you built the base at your homeworld, going from 110% to 140% alliegance is usually good for an additional 4.5 creds/sec. the culture thing is less useful in my opinion since its extremely hard to culture flip a planet anyway, but if you're really pushing that strategy you can get massive culture spread out of a starbase. its a bit too slow for my tastes though so i never use it. 

A few thoughts on the Advent:

Integrated Defense:

Like their ships, the Advent Starbase needs support id you want them to have much staying power - that means upgraded beam cannons (preferably in clusters of 5), several regeneration bays, and several hangarbays (with fighter and sheild upgrades). If you layout your defenses correctly all of your defensive unitis inculding your starbase are much harder to kill. 

Economy:

Maximising your alligance on key worlds is a massive boon to your economy and adding merchant upgrades to starbases in noncolonizable gravity wells extends your trade chain to unbelivable lengths.

Culture:

Besides being absolutely neccissary for your own economy, Advent Culture is your superweapon. If your playing a game long enough to get to super weapons you've had time to build starbases with culture upgrades which don't just spread your culture but repel enemy culture. The key is to get these upgrades early in worlds near but not on your front line. As the game progresses your neigbors will have to invest in lots of cultural centers on their front lines to counter your cuture or lose their front line worlds. This eats up their resources, logistical slots, and dampens their productivity. In large games your culture will quite literally create a buffer zone of worlds taken over by your culture. Combine this with Advent Upgrades and you have the best intelligence in the game. You know where and in what size your enemies are if they are in systems dominated by your culture or 2 jumps away from your systems. Thats a huge advantage when planning strikes or defending your territory. 

In general you've got to realize that star bases are part of a long run strategy that out produces and out culture's you're enemies. They don't survive on their own as defensive structures. They require an integrated defense of support structures and fleets - but are very effective when you take a wholisitc approach to defense.

I do like the synergies with other tactical structures too.  Plus Advent gets tactical upgrades through research. 
So whereas TEC has a logistical advantage, Advent gets a tactical advantage perhaps?

When used properly, TEC's "detonate" can turn the tide of the battle. the only problem is that its rather difficult to use effectively. A few days ago, i blew up almost an entire fleet with that ability, leaving only a few ships to mop up with the rest of my fleet. It was a gamewinner, and the enemy never really recovered.

so bottom line, dont be too quick to judge a large, suicidal space bomb

Yes, the TEC starbase can be extremely useful. But the point is that it's necessary for the enemy to actually engage it. Unless there's a bunch of carrier huddling close to it I can't see any sense in doing so. Just pass it by and attack your target of choice. That is why I never build starbases as TEC, or rather only as a last resort in the hope that my enemy engages it. Vasari SB can move, the advent got a fairly long-ranged meteor strike whereas the TEC...blow up their crappy construction. It's like a giant mine...useful if someone gets too close, but basically against a skilled opponent not much more than space decoration..

Wormhole.  Star.  Cooperation with an Advent ally using Repulsion to bounce enemies to your starbase.  Defense in depth so that an opponent doesn't want to run smack into your next defensive line with loss of 30% HP and 100% AM.  An Advent ally base built only to Mass Disorient a fleet so it can't get out of range of the TEC base blast.  And so forth.

i like the culture thing only when i have the upgrade that lets you see planets under your influence of culture. in a long game, its even better then highly attuned sensors at finding stuff

I did some testing with the Tec suicidal base.  It has a timer after activation, so a player still has time to flee.  The blast radius wasn't very big either.  The 4k damage will not be enough to destroy a Vasari base, and the blast can damage your own units and structure.  If all that wasn't bad enough, you have to spend one slot for the bomb.

I didn't know that.  Was wondering why its possible to put 2 points in.

For the love of God, no.

The Vasari base is the only one that moves (in the gravity well), and the general consensus is that it will remain that way.

Be smarter about where you build.

Also Starfishes are great.  They don't hit as hard as their TEC counter part, but they can hit several targets at once.  Combine that with range and you have a demolition crew.  Build a couple and run them into enemy bases and you will see.