Quasars and Gamma Ray Bursts
I think you may be mixing up "Energy" and "Power" a little here. Power is the rate of Energy output per time. If Power is the speed, then Energy is the distance travelled.

Quasars look like stars, from Earth, they give out a light, and while they do vary a little (or a lot) you would not expect to see new ones forming or existing ones fading away.

Gamma Ray Bursts are a short lived. While a quasar will emit more energy over it's long life. Gamma Ray Bursts are more powerful. They are formed mostly as a result of energy released in gravitational collapse during a hypernova. Moreover this energy is released in a narrow beam. 

Imagine comparing a laser beam with a equivalent power light bulb.  If the laser is pointing right at you, it appears much brighter than the bulb.

So the answers:


GRB are more powerful than quasars, but only last a short time.
GRB are form a beam of radiation.
So if a GRB and a quasar are equally distant, the GRB would appear brighter.