I don't think Advent really has a good response to this at all.  Against massed Javelis you could go with defense vessels, but any TEC worth his salt will anticipate this and have diversified enough to counter it with ease.  Illuminators are pretty much useless once hoshikos are on the field, disciples get trashed by LRM's, and drone hosts are so easily countered this early in the game it just isn't funny.  You're basically stuck leaning on the Halcyon for dear life, and the destra is basically a shining beacon of hope; good against LRM and capital ships, great at focus fire to downplay the power of hoshikos, and protected by their only counter (bombers) by your Halcyons.  Really, I see no reason for Advent to do anything except bee-line for destras in the current version of the game.

4's and 5's yes, 1v1 I'd say no.  Reason being is that random 1v1 has a tendency to create long stringy chains of planets, whereas the larger random maps tend to create dense clusters of planets.  This means the 1v1 map lends itself more easily to fast trade (though in the long run, the sheer size of a typical 5v5 map means trade becomes godlike).  However, it all comes down to how the map randomized.  One neutral blocking your chain can cripple early trade, while a string of roids makes it pretty much an auto-win if you play it right.

I can attest it's very difficult to create a 1v1 map that doesn't favour Vasari.  I think we actually have a good selection of maps that are fairly good for TEC vs Advent (I like Derelict; a bit too random for competitive play, perhaps, but for TEC vs Advent or Vasari vs Vasari a very good map).