Doing the firebase white geth/gold thing, I can make it through entire rounds w/o firing a shot with the Asari Adept if I so choose. The same with an engineer with overload and incinerate, though not as effectively as the Asari Adept.
There seems to be more powers that work and get you out of sticky situations than weapons. The Black Widow is an excellent weapon, but doesn't really help too much with phantoms, or a rush of geth pyros/hunters during an objective round, for example. In that
situation, you can blast away with a Carnifex or Saber and in my experience it doesn't increase your odds of survival near as much as good powers will.
There are some cool guns, but powers win for me. And as somebody mentioned, if you know how to effectively combine the two you are unstoppable. I like to release the throw power, and fire two rounds off with the carnifex before throw gets there so that throw
finishes the job. Makes me feel like a bad mamajama
Depends on the class you are using. Soldiers and inflitraitors fare much better with weapons, as they have skills tailored for them. Adepts and Engineers pretty much live off of powers to do most of the mopping up / supporting.
Vanguards and Sentinels can be very balanced depending on your build, but i know for a fact that when you spec them in Power damage, they tend to fare much better than wth a weapon focused build.
Why settle for one or the other? If you have both - great weapons and know how to maximize your powers - combine those strengths and you'll be unstoppable (or at least have a lot of success and enjoy the game). That will net you the best bang for your buck.