One race is able to make up for its light long range frigate with a strong economy to build lots of them, the other makes up or its expensive ships by having stronger and harder ships to take down along with moderate dps weapons that bypass shields but also an economy that builds up from the beginning with resources to the end with trade.
Meh. In terms of DPS per supply and per resource cost, the ships of the different factions are quite similar, although Advent's frigates are slightly more powerful in this regard.
But pure DPS isn't everything, of course - Advent's better frigates still result in a huge weakness to large targets (caps and starbases)
Late-game Advent with abilities will be very strong against TEC which can't do much then other than trade and spam more. Still, Advent's bad hulls/armor and weak caps make it very easy for Vasari players with Phase Missiles to decimate them.
Overall in any war the economy will determine the victor and having a stronger economy with strong deadly ships wins the day.
Not always, especially not in the late-game. The key is balancing investment in your economy with investment in your fleet. In the early-game, you might have gone for trade in a 1v1 while only having basic defenses, but even if you're getting 28 creds/sec and your opponent is getting 20 creds/sec (almost a 3:2 advantage), if the enemy has 2 or 3 caps bombing your front-line world, they're being more effective and you'll be significantly more likely to lose the game despite a much better economy.
After the initial rush period is over and players have moderate fleets, economy is definitely the most important factor, and the player who can pump out ships which deal the most damage for their cost can often push the enemy back and win, due mainly to superior economy.
But then as the game progresses on, fleet firepower grows to eventually become even more important than economy. When each player has 100-150 frigates on the battlefield and ships are dying every couple seconds, a somewhat superior economy isn't necessarily going to win you the game, especially if your fleet is outmatched by more than a small amount. Even with a superior economy, it takes time to build ships, and if the enemy fleet pushes yours back onto your world with frigate factories, if the enemy manages to destroy your frigate factories while building more ships of his own, you've taken a very significant loss and have probably lost - you can't replace your fleet fast enough while the enemy pursues your fleet and destroys it (while his caps bomb your worlds)
Tec and Vasari can always be on the offensive however advent tends to be defensive from an equally expensive illumminator compared to assailants. Given room to build an economy an advent fleet can (when projections are micro'd with vertigo) take a pounding and still win the battle-but those are stories people tell to their friends to scare them. Rarely happens.
Advent can be extremely effective offensively if players are close enough to attack within the first 5-10 minutes. Scout-Disciple spam is plain but can be very strong early in the game against enemies who aren't completely prepared for it. I've seen many, many games where a skilled Advent player goes on the offensive and overwhelms an enemy's HW in the very early game.
If the Advent player doesn't do that for whatever reason and has to wait even a few minutes though, they can quickly be put on the defensive once other factions have had the freedom to research initial techs and build up a moderate fleet and to potentially threaten with Orkuluses. Since Advent don't really have similar decent initial tech to invest in they often have to defend.