Better LRM
In terms of raw combat power, that's a definite yes. However, as Amish has already mentioned, the assailant is a shocking capital ship assassin.
Better Flak
Not really. The defense vessel deals more damage, but the sentinel receives a pretty potent special ability. The sentinel is slightly tougher, but slightly more costly. Seems roughly on par, certainly not a measurable advantage.
Better HC
This is another arguable point. On a per-command basis, the enforcer deals slightly less damage, but has slightly more health. It certainly has the better special abilities, but its attack upgrades are more expensive. Again, seems like a pretty evenly weighted situation.
However, it's worth noting that the destra is at its worst in the vs Vasari matchup. Between phase missile bombers and nanos, the destra is really vulnerable. In fact, I usually upgrade all my hull research before bringing out the destra against a Vasari opponent because nanos kills them so easily otherwise.
Better Caps
In a general sense, yes, the Advent have the best capital ships in the game. On the other hand, Vasari are hands down the best capital ship killers.
Better support cruiser (gardian)
Goes without saying. That thing is a monster. That said, Vasari do have the best tools to bring it down.
Better late game econ then TEC
Where'd that come from? The opposite is true! Advent have by far the weakest economy (aside from their early game boost courtesy of the progen), and their only saving grace in the late game is allure of the unity. Great upgrade, but the TEC and Vasari have better. Their mid-game economy is an absolute wreck, since there's largely nothing between trade ports and allure.
Basicly better everythign in the end right?
I've always found Advent an interesting faction. They've got the best weapons and the best shields, coupled with the best auxiliary support. In other words, the best standing fleet. However, they have a lot of outstanding issues. The most obvious in the vs Vasari matchup is they have on real way to deal with shield bypass. It absolutely wrecks havoc on the Advent, and is only made worse by the fact that their repair cruiser is borderline incompetent and expensive to bring out. They have a shitty economy, the only real advantage being the benefits offered by the progen.
Advent have one final weakness that's very important to remember: they are utterly dependent on their support cruisers and capital ships. Disable, destroy, or route the guardians or the progen and the entire Advent fleet is going to be in full retreat.
I also notice we're not even going to bother comparing the disciple to the skirmisher. Kind of strengthens what I've been saying around here for some time: the light frigate just doesn't have a substantial role within the larger fleet.