If you need the extra 10 tac points for defense as Vasari, then the phase stabilizer upgrade to the SB might be worthwhile.
Unfortunately, no. Prior to the 2.5 update, yes, you were better off using one SB slot for the stabilizer and using the ten spare tac points for two hangars and a nano jammer (or PJI if you didn't have one yet). This was ESPECIALLY true back when SB hangar upgrades only gave two squadrons, but even now with them giving four, it'd still be a worthwhile tradeoff if the stabilizers still worked the way they used to (always on); you'd be gaining two tac points (8 vs 10), not to mention the extra benefits hangars now give. (Also, putting a stabilizer on a starbase around an asteroid was great as it let you use 18 of the 25 tac points for a Kostura without making the roid unreachable by your response fleets.)
But after 2.5, it's not even close; stabilizer structures are now FAR superior to the SB-mounted ones IMO. There are two basic reasons for this:
1> The structures are always on. No need to activate them by hand, no need to spend AM that could be used for deflector shields. Also, IIRC the current stabilizer is a channeled ability, so if the SB moves during the process you lose the gate...
2> The structures can summon reinforcements (if you have the tier 8 tech, of course). SB-mounted gates can't do that. However, you only really need a couple "normal" gates to do this, as you can then send them to the planet of your choice fairly quickly, so it's not a huge loss to ignore this factor; you'll have a few normal gates around back-line systems anyway, in systems you colonized before you had the cash for starbases.
The biggest downside is that an enemy fleet can blow up the stabilizer with carrier bombers without having to whittle down twenty thousand HP of a heavy-armored mobile starbase to reach it. Against the AI this is a non-issue, against a smart human opponent it could be major. But I'd still rather go with the always-on structure, simply to save on micromanagement.
Again, though, this is only about "defensive" starbases. If you're building an "offensive" base, i.e. in someone else's system, the structure isn't an option. But even there, the Kostura IS an option, and a generally better one at that. Sure, its fire rate sucks, but the damage+stun is tremendously useful in its own right. Plus, it frees up the eighth slot in those offensive starbases for more offense/defense.
Ironically, then, the best use for the SB-based stabilizer is in truly neutral wells. That is, asteroid belts, plasma storms, wormholes, around stars; anywhere there isn't a planet. That's because you simply can't target those with Kosturas and can't build stabilizer structures, so the SB stablizer is literally your only option.