The main difference between automatic watches and the battery-powered watches is the built-in movement.
The automatic is powered by a mechanical movement via spring tension. Inside, a rotor moves along with each movement of the arm, tensioning the spring. The spring then transmits the force to the hands via the mechanism. So the automatic runs completely without a battery - you can wind the spring both by moving it on your arm, and by manually winding the crown.
If you don't wear an automatic watch for a while, it will stop until you wind it again via the crown and start it up.
In a quartz watch, the electrical voltage from the battery is passed through a quartz crystal, which acts as a 'clock' in the movement, regulating the energy that is passed from the battery to the hand via the gears. This is what makes quartz movements run so accurately with the simplest construction. So if you're more after a straightforward option that only needs to be set once and then runs through, I'd recommend a quartz watch.
One of the main reasons to choose an automatic watch is the technical precision needed to run a watch completely without battery, and a mechanical watch also scores in terms of sustainability. In addition, many of our models have a visual advantage, because the glass back allows you to watch the mechanics of the automatic watch at work.