conventional wisdom (which is largely true in my opinion) is that from a military perspective the three factions are very closely balanced. the Advent do fine in the first 3 or 4 tiers of civilian research as well. the most noticeable place they are lacking is in tiers 5-8 of civilian research. Vasari and TEC get super research like Returning Armada or Pervasive Economy where the Advent have no comparably strong civilian technology. 

regarding military balance i think alot of people really enjoy the Advent style. its very effective, particularly rewarding for players with good micro-management skills. The illuminator is the best Long Range frigate if you're good at positioning them. Guardians are probably the best defensive support cruiser if you're good at using Repulsion. Advent squadrons are slightly better than other races squadrons (though slightly more vulnerable to Flak Burst from a Kol, but thats not a big issue really). 

i'd never say Advent is nerfed. i'd say that in the latest stages of the game they fail to compete with end-tier civilian research so the best strategy is to push military very heavily in the mid-game. call that a balance flaw if you want, but i don't see it that way. its just the way Advent is. 

As everyone pointed out, Advent is very good for a player who likes to micro manage all the special abilities they get.  When I play them I rarely make more than 4 or 5 civic labs...and the benefit of this is that you can just focus on your military tree while other players are working on their civic tree.  Just build trade ports everywhere....the Advent economy does just fine as long as they build tradeports at some point.

Advent also has some of the best defensive options in Entrenchment.  Homing mines, shield upgrades for defensive structures, and a very nasty Starbase if you research all the tech upgrades for it.

Definitely maxing out reactor upgrades is a better investment than the recharger.  The problem with the recharger is that it costs a lot of resources to get all its upgrades, and you need lots of civilian labs.  Just not worth bringing out until later on.

Advent has only two real weaknesses.  The first is that their civilian tech tree is sparse after level 3, and their economy isn't as versatile as a result.  If you spam trade ports, they'll do just fine, but you don't have much option with regards to refineries or such.  Secondly, they're a little shield dependant so Vasari phase missiles can give them trouble.  Other than that, they're very solid and powerful.  You just have to be careful to micromanage them effectively.