How a mechanical watch keeps time
A mechanical movement stores energy in a mainspring. A gear train transmits that energy to an escapement, which releases it in controlled increments; an oscillator regulates those releases. In an automatic watch, a rotor turns with wrist motion to wind the spring. A manual-wind watch is wound by turning its crown.
Mechanical rate depends on adjustment, position, temperature, lubrication, wear and daily use. A certified chronometer has passed a defined test, but certification is not a promise that every watch will keep identical time on every wrist for its entire life.
How a quartz watch keeps time
A quartz movement uses an electrically energized quartz crystal as a stable oscillator, with a circuit counting its vibrations to drive the display. Most conventional analog quartz watches use a battery; solar-powered quartz models collect light, while other designs use different power systems. These are still quartz timekeepers.
Quartz watches are generally more accurate than ordinary mechanical watches and often require less frequent maintenance. Batteries and seals still need attention, and sophisticated high-accuracy quartz movements may have their own service requirements.
Choose by how you want to own it
Choose mechanical if you enjoy winding, the motion of a rotor, the sweep of a seconds hand, movement finishing or the continuity of traditional watchmaking. Choose quartz if you want a watch that can sit unused and still be close to the correct time after its power source is maintained, or if high accuracy and low fuss are priorities.
Price is not a reliable way to distinguish the categories: both mechanical and quartz watches span a wide range. Judge the particular movement, case, dial, finishing, warranty and service plan instead of assuming one technology makes a watch luxurious.