Okay: So I want to give my take in one place, where it won't be immediately drowned out by the volume fo response. To avoid some problems I'll post some basic points that I DONT want or care to talk about.
1. This is not AT ALL about the Vasari being over or under powered.
2. I believe virtually everyone realizes the Vasari are too weak in the early game, and that they are too tech dependent, That is also NOT an issue I want to discuss.
3. I'm going to try and avoid talking about the various 'Vasari ships should be better but lesser' issues and opinions, lets basically assume that what I am talking about is not going to be related too too much to the ship stats.
SO- What I think the Vasari could do/have that would make them different and closer to the lore, without directly affecting their military play.
Colonies:
The Vasari are mobile, in fact everything I am going to suggest will relate to this mobility, the Vasari want slaves and resources, they don't want a new empire.
So- the Colony Ship of the Vasari should actually BE the population center, with a very very low growth rate when not attached to a planet (maybe have it start with 10 pop, and it just never grows) The ship would attach to a planet. It would also be expensive, you would then grow population on board the ship up to say 20, but the remainder would be on the planet. In addition the Vasari wouldn't build mines, the Colony Ship once deployed would send tiny little nano-fleets that would mine the asteroids periodically based off anti-matter.
Why do it this way? Because it wastes less resources: The Vasari need resources, why waste it building mines you eventually abandon? Why risk their population on the planet covered with slaves? The better crop of soldiers and scientists would stay high above in orbit, ready to repress the population with bombardment. The Colony ship could even be the Vasari siege frigate! Sounds great doesn't it?
When detached, the ship can't mine resources or grow more than 20 pop, pretty low, and the ship itself would be pretty expensive, though not too expensive in fleet supply hopefully.
What would the detractions be? Well think about it: While the ship can detach and evacuate a attacked world, the moment it does your empire lost 2-3 mines, and the planet below would be easy pickings (I would reduce the Vasari ability to upgrade planets drastically, why would they bother? they plan on leaving.)
Its an 'all your eggs in one basket' deal, your colony, and your mines are on one big slow target, with no or absurdly weak weapons. The TEC could raid the Vasari to death very easily with numerous small fleets by targetinging these, it also means you could destroy significant planetary value without Siege Frigates, making the offense for the TEC very very different... they would still want to siege the planet later, but they could cripple the Vasari without them. By taking out the Vasari Siege Frigate, and combining it the colony ship it also risks a larger investment for the Vasari at war, the Tec may lose the battle but sneak in and destroy your expensive all-in-one colony/siege weapon. Making it a pirate victory for the Vasari.
Idea 2:
Production methods:
The Vasari seem to rely allot on nano-technology: thats awesome, why not use it better? The Vasari Refinery, like their colony should be mobile, but incredibly slow, on top of that, it should also repair nearbye ships. Making it a great defensive structure. It shouldnt be able to move and build; it should again be deployable, and have a big cool-down once made stationary, allowing it to be quite vulnerable for a time, but with forethought the Vasari CAN evacuate it. On top of that, I would alow a technology upgrade allowing it to build more than one ship at once... because the nano-bots build the ship in open space, so upgrading the facility to build more nano-bots would let you build more ships in open space. That would be very very neat. Overall this approach would let you save a tiny ammount of logistics points, as both this and the colony would use fleet supply. Allowing you to build more labs with logistics.
This would allow the Vasari to move their production forward, again a mobility advantage over the TEC strong arm. The whole point of these ideas is to avoid the debate about 'Vasari should be stronger' junk. If their advantage is mobility then truly give it to them!
Carriers and Fighters
Why do the Vasari risk such valuable population manning such things? This would be a great way to differentiate the Vasari, eliminate their fighter/bomber wings entirely, and make the Carrier a dedicated repair and support ship... hell, the regular shipyard could stay and the Vasari Carrier could become the shipyard I mentioned above.
To account for their lack of fighters, all Capital Ships would have a low range AA gun of some sort, and of course they can research their flak frigate. This would make them different and seem numerically lesser than the TEC without trading much at all. The Hangar can be replaced with a Laser fortification that zaps fighters, like a bug zapper.
Defenses
Since in this system the Vasari have no fighters/bombers, overall gravwell defense is tricky, so give them a MOBILE defense platform, it could be very slow, but the ability to move in a long battle will be very important and give them a bit more gravwell control, as well as making more sense with their general concept of 'masters of war'
Any good tactician will tell you static defense died a grim death in WW2, and in space this is even more true... only the stupid TEC would have stationary defenses that can easily be outranged! (Damn them for having disposable capital and pilots for fighters though!)
Finally:
We all know its too late to really implement things like these ideas. Some of us are very disappointed in the lack of unit differences, some don't care, and some are right when they point out that it really doesn't matter too much.
We all know the Vasari as the Devs imagine them, have the advantage not in brute stregnth or numbers, but in mobility and intelligence. The problem I am seeing is that these stregnths do not PERMEATE Vasari game-play, it isn't pronounced, and it is more than a way fo war for these people... its a way of life! Sadly this is not reflected in the Vasari.
I'm not trying to make the Vasari the Protoss, which is the big OTHER debate going on. I'm trying to make them more Nomadic, which means highly mobile, including infrastructure, but at the same time highly vulnerable and fragile if and when they are finally tracked down and caught. A good Vasari player with the above modifications will have to constantly observe the enemy and moving his shipyards and occasionaly evacuate colonies...
Thats not neccessarily an advantage!