There's more to a move than just the damage. There's a speed factor that affects the overall DPS. Faster moves also make it easier to dodge.
The moves have three main characteristics to them: Damage, Speed, and Type.
Damage is the number next to the attack, showing how much damage it will do to an enemy. Type is shown below the name and is used when determining type advantages for additional or reduced damage. Speed doesn't not seem to appear anywhere, but it determines how quickly your pokemon can attack.
For speed, I need to do additional testing, but there are some attacks that obvious attack at a faster rate. My Pinsir attacks at blinding speed with Fury Cutter, much faster than my Pidgeot's Steel Wing. But you should note that Fury Cutter does 3 damage while Steel Wing is at 15.
Therefore, it is possible for a lower damage skill to actually out DPS a higher damage skill.
Another important aspect is dodging. If you are using a skill with a long wind-up, your pokemon cannot move for that time. That leaves you vulnerable to attacks. Having a fast move will make it easier for you to react to and dodge attacks. Therefore, even if the DPS is lower, it might be worth it to use the faster, weaker moves.