I find I have to make a pretty large device to have anywhere near the same power as the human hand.
Is the human hand, cubic centimeter for cubic centimeter just really strong compared to a machine?
Keep in mind that power and strength (force) are very much separate things.
It is easy to make a very strong and small gripper, by using worm gearing to magnify the force of a small motor. The limit is the strength of the materials used. Human bones and tendons are pretty strong, but there are engineered materials that are even stronger for the same size.
As for power (work done per unit of time), one cannot look at the hand in isolation. Like Andrew mentioned in a comment, the muscles are actually in your arm. And the cooling and energy supply are all over your body. To compare, a hydraulic gripper can deliver very high power in a small space because it offloads part of the work to the hydraulic pump supplying it.