Vasari is kinda the middle ground between Advent and TEC. TEC Capital ships are very direct in what they do. Advent capital ships are the nexus of support for an Advent fleet. Vasari are right in the middle. Still critical to a fleet, but still pretty direct. An ability like Nano-disassembler, the nanite bomb on the Egg, is a good example. It deals direct damage to a ship, but lowers its armor too so it's a better target for the rest of the fleet.
Advent easily have the best caps in the game. They do so much for an Advent fleet. To call Vasari caps, or TEC caps for that matter, bad is just not a fair statement. All caps have some way to be exploited.
I'm feeling a little lazy so I don't want to look up all the names of the ships, so I'm just going to go in the order the caps appear in the in-game view screen.
Battleship (Devestator)
This ship is an absolute beast. This will win 1 v 1 with a Kol because more of its weapons are in the front. This ship has two meh abilities and two awesome abilites. The first ablitity, Power Surge, and second abilitiy, Jam Weapaons, are ok, but tnot game changing. The third ability depletes antimatter, quite useful against someone reliant on antimatter, such as say Advent or a Sova rusher.
The lvl 6 ability, Volatile Nanites, is one of the better ones in the game if you can get it to work. When a ship gets destroyed that was effected by the nanite, it damaged everything near it, setting up a chain reaction.
Carrier (Skinatra)
Quite uesful if you're massing fighters. The repair cloud will heal everything, including the Vasari's trademark tough fighters. Unfortunately, repair cloud isn't that useful for a fleet because to heal something, that ship has have lost its shields, so if you activate this ability in battle, you're likely only healing said targeted unit. Scramble bombers is meh, but the passive buff that helps the fighters is ok. Keeps 'em alive longer.
The lvl 6 is actually very good. You can clone your own units, but what's great is that you get three, not one unit, at least that's what I think it does. I've never bothered to get this to level 6, but this is what I've read.
Colonizer
Oh my how I love the space egg. This round ship has colonize, meaning you can expand quickly early with this ship. The gravity bomb is nice, but the nanite bomb is a beaut. No enemy capital ship is safe when you have this ability.
To top it off, the lvl 6 turns it into a sieging machine that gives you resources.
Support
This ship is getting a massive buff in the coming 1.1 patch. As this ship stands right now, all of its abilities are rather bleh. Phase out hull is great for negating an enemy ship's presence OR saving one of your ships that's being microed. People undervalue distort gravity, for ships affected by it ignore phase jump inhibitors. What's getting a huge buff is subversion. This ship will personally be able to ruin the "factory planet" that someone chooses.
Sieging Cap
It gets a passive buff for sieging, and a siege platform to help it siege. YAY! What most people don't realize is that seiging platform is actually as effective as the TEC Marza Dreadnaught. The damage per second is very close because the Marza does all its damage very quickly. The Vasari one does it over time consistently. The phase missle swarm really is kinda bleh. I like it early, but in late games where the enemy fleet is huge, this ability is just kinda weak.
The lvl. 6 is unique. You can leech hull points from enemy ships. Rather useful actually.