In competitive play a lot of vasari power in first 15 min relies in how map is set up (neutrals, choke points etc) 

And no picking right race it is not instant win button. There are some threads about who is strongest early mid and late game. Although some would argue that if game comes into late game and vasari are in decent shape they can become unstoppable but only if you play towards their strength and you know what other races strengths are and not walk into traps.  

I play advent almost exclusively on ICO.

Superweapons aren't usually an issue in competitive MP play though they do come out sometimes.

The competitive games to play are 3v3, 4v4 or 5v5's. These games are fairly fast paced ending when it's clear one side has lost to the other (i.e. people don't play to the last planet like against the AI).

Balance right now is skewed towards early game Light Frigate rushing though a balance tweak has been made upping the counter for LF from 1.33 to 1.5 (Affects all Long Range Frigates against Light Frigates).

A couple of other balance changes have been added as well that will have some good impacts overall.

Sins goes through periods of varying degrees of imbalance... honestly as far as faction balance is concerned I think its one of the best balanced in Sins history, which is impressive given all the stuff the expansions have been adding. However when Rebellion was first released it was pretty bad, so if you're reading older threads that probably explains that.

Yes there is still some concern about the Vasari, though they are infinitely more balanced than they were a year ago. Their ridiculous new Rebellion capacities are now at a more balanced level, its just their long standing late game tech advantages like phase gates and phase missiles that keep them in the number 1 spot. In the days of the original Sins this did not matter as much, since the Vasari had very severe early game disadvantages, so they were very much a race that was awesome if you survived but you were likely to die early. However, things like buffed Vasari capitalships and early offensive starbases and even quick start have made it far easier for competent Vasari players to survive until the late game, so there is not as much risk to playing them as there used to be.

The only reason Advent is considered the weakest is also because Vasari phase missiles hit heavily shielded units, like all the Advent's ships, much harder than anyone else. If someone made a mod where phase missile techs just increased damage instead of shield bypass chance I think the three races would be very close to each other indeed.