This is the first decision in buying a watch and it is usually made badly, because the arguments on both sides get overstated. Quartz is not "soulless" and automatics are not "better made." They are two different technologies with a clear and measurable split: quartz wins on performance, automatics win on everything that is not performance.
A quartz watch keeps time by passing a current through a quartz crystal that oscillates at a precise frequency. An automatic watch keeps time with a wound mainspring released through a balance wheel and escapement, and winds itself from the movement of your arm. That is the whole difference; everything below follows from it.
The short version: buy quartz if you want an instrument — better accuracy, lower cost, no servicing, and no watch that stops in a drawer. Buy automatic if you want the object — a mechanism you can have serviced indefinitely, a sweeping seconds hand, and something that is interesting rather than merely correct.
Accuracy: quartz wins by roughly a hundred to one
Seiko rates its 4R36 automatic at approximately minus 35 to plus 45 seconds a day. A standard quartz movement is typically specified in seconds per month. That is not a close comparison and no amount of money closes it — a chronometer-certified mechanical watch is rated to within a few seconds a day, which a cheap quartz beats comfortably. If knowing the correct time matters, the decision is already made.
Maintenance: quartz is a battery, automatic is a service
An automatic needs periodic servicing — cleaning, fresh lubricant, new gaskets — typically quoted every five to ten years, at a cost that on an affordable watch can approach a meaningful fraction of the purchase price. A quartz watch needs a battery every few years, which on a water-resistant case should be done by someone who can reseal and pressure-test it. Solar quartz, like Citizen's Eco-Drive, removes even that.
Lifespan: this is where automatics earn their reputation
A mechanical movement is made of parts that can be cleaned, adjusted and replaced individually, so a well-kept automatic can run indefinitely — this is the genuine argument for buying one. A quartz movement is usually a sealed module that is replaced rather than repaired when it fails, and modules for older watches eventually stop being made. Over fifty years the automatic is the survivor. Over ten, both are fine.
Water resistance and toughness
Nothing about either technology limits water resistance, and the highest-rated watches on this site include both — the Casio Duro is a 200m quartz and the Seiko Turtle is a 200m automatic. Quartz does have a real durability edge in one respect: fewer moving parts to knock out of adjustment, which is why the toughest watches in the world, G-Shocks included, are quartz.
Cost, and where the money goes
At any given price a quartz watch has more budget left for the case, crystal and dial, because the movement costs a fraction of a mechanical one. That is why a sixty-dollar quartz can have a 200m case and a sixty-dollar mechanical cannot exist. It is also why, under about two hundred dollars, we consistently recommend quartz — you are buying a better watch, not a lesser one.
The one thing quartz cannot give you
A sweeping seconds hand and the knowledge that the thing on your wrist is a machine powered by your own movement. That is not a rational argument and it does not need to be. Most people who become interested in watches become interested in mechanical ones, and if that is you, no accuracy figure will change it — nor should it. Just buy the automatic knowing precisely what you are trading away.
What we would actually do
Own both, and stop treating it as a single decision. A quartz or solar watch for the days you need to not think about it, and an automatic for the days you want to. The two together cost less than one mid-tier Swiss watch, and it is the arrangement most people who own several watches end up with anyway.
