While an untrained fighter might swing at you using only their arm strength, a person trained in Karate will use their arm, shoulders, hips and legs to generate power. The fact that their entire body is acting together allows them to hit harder than their inefficient larger opponent. Likewise, Aiki-Jujitsu is based not on strength, but on breaking the opponent's balance. Once the opponent's balance is broken, it becomes much easier to throw them since the Earth's gravity is assisting you. Furthermore, very few people know how to mount a counter attack once their balance is broken.
Every throw starts with a balance break.
All this being said, it never hurts to be stronger, faster, and more flexible than your opponent. There is no instantaneous transformation from beginner to black belt. Many of the techniques used at black belt levels are simply combinations of techniques learned at entry level. The differences are in how well the technique is executed and in what combinations they are performed. As you rise through the ranks you tend to get more efficient in your techniques.