An automatic movement is all mechanical and requires no winding because the rotor (part of the automatic mechanism) winds the mainspring by the movement of the wearer’s arm. Most mechanical movements are accurate within one minute each day and have reserve power when not worn of at least 24 hours.
A quartz movement is made from natural or commercially synthesized silicon dioxide rock crystal. When activated by a battery or solar power, the thin sliver of crystal very predictably vibrates at an extremely high frequency thus providing very accurate time, with a degree of accuracy that deviates no more than one minute a year.
Mechanical movements, usually the domain of more premium watches, are inherently more complicated and expensive to produce and will not tell better time than a quartz watch. However, automatic movements are prized for their craftsmenship, as jewellry, and as collector’s items.