There are many reasons for this and many ways to get around it. Maybe your form of running favors one side by over-refracting certain joints. You may have a muscle imbalance that causes your pelvis to tilt and the muscles around your knees to shorten.
That means your knee hurts when the joint moves, not when it's loaded. Compression helps in both cases, but knee compression sleeves for knee ache tend to be most helpful with movement-related pain.
In competitive powerlifting, there are two categories in which competitors can compete: raw without a knee wrap and raw with a knee wrap. The knee wrap helps the lifter crouch more by resisting flexion and helping them move. In other words, when the lifter's knee bends, the sleeve struggles to keep the knee straight.
Knee cuffs work the same way, but to a lesser extent. Wearing knee sleeves doesn't necessarily straighten your leg, but it will help it unfold from a fully flexed position – when the knee is most vulnerable.
The best knee sleeve for you depends on your type of activity. For general activities and light exercise, a thinner, more flexible arm will suit you. For more strenuous activities like weightlifting, a thicker, tougher case is best.
It is important to consider your activity and injury needs when determining your optimal rehabilitation program. Nothing can replace a medical diagnosis when you are injured, but careful athletes with the right tools can easily stay pain free.