They want all parts of the work to be equally interesting. Harmony - complex but pleasing visual combinations are harmonious. Unity - when nothing distracts from the whole you have unity. Unity without variation can be uninteresting - like driving through western Kansas on the interstate. Balance is the consideration of visual weight and importance.
Symmetrical balance implies that both sides are the same.
Gothic cathedrals are often symmetrical with their central emphasis pointing to heaven. Asymmetrical balance is more interesting. Both sides are the similar in visual weight but not mirrored. Radial balance is not used much, but it is like a daisy or sunflower with everything arranged around a center. Rose windows of cathedrals use this system.