Short answer:
Quartz watches are powered by a battery and regulated by a vibrating quartz crystal, while mechanical watches are powered by a wound spring and a complex system of gears.
Quartz Watches
Quartz watches operate using a battery that sends electricity through a quartz crystal. The crystal vibrates at a very precise frequency, allowing the watch to keep extremely accurate time.
Advantages:
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Very accurate
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Low maintenance
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Affordable
Mechanical Watches
Mechanical watches rely on a mainspring and gear system rather than electronics.
Advantages:
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Mechanical craftsmanship
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Long lifespan if maintained
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Collector value
Which Is Better?
Neither is objectively better. Quartz watches prioritize accuracy and convenience, while mechanical watches focus on craftsmanship and tradition.