When you have the thrust levers of, say, a 747 all the way back to idle, the airplane still has enough power to move. In fact, you will have to use the brakes to keep it from taxiing too fast. If you didn't use the brakes, it would finally accelerate to somewhere around 45 knots or so, far too fast for taxiing, but much too slow to take off. At the idle power setting, relatively little noise is produced by the engines.
To take off, if the 747 were at max gross, you would have to accelerate to around 180 knots. That would require a power setting approaching the maximum, depending on the length of the runway. The noise produced by the engines is relative to the amount of power they're producing. Hence, taxiing at idle produces little noise relatively speaking, on the runway taking off a whole lot of noise.