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A quartz watch is cheaper and more accurate than a mechanical watch. A good mechanical watch can typically be made no more accurate than 2-3 seconds per day. Your typical inexpensive quartz is usually good to 0.5 seconds per day or better. But when you talk of mechanical watches, craftsmanship, aesthetic and tradition are the key attractions, rather than just accuracy! Because the wheel train of an analog quartz watch is not under constant stress from a wound mainspring, it does not need to be as finely finished, nor does it require painstaking skill and precision in assembly.
In respect to durability, a quartz watch is much better on shock resistance over the mechanical, but it is certainly not invulnerable. Low mass of the vital components helps protect them from shocks. The balance wheel's cap jewels, the balance staff, the rotor bearing (in an automatic) and various other parts of the escapement, especially cap jewels are the vulnerable parts in a mechanical watch. Moreover, a quartz watch has few moving parts, which implies, lesser friction and lesser wear and tear. Mechanical watches need to be maintained in good condition.
In terms of reliability, the mechanical watch has a history attached to its name and make. Though, this can be true of a quartz, the battery is a slip. Battery life is not predictable. A mechanical watch can withstand extreme temperatures, unlike a quartz watch.
Replacement parts for mechanical watches are available; you just need to make sure that they are original. But when it comes to age-old quartz watches, the batteries would have become obsolete, which means, that old quartz watches are just matter of memories.
Apparently, mechanical watches can last longer, provided they are taken care of and serviced well. Also, if in good condition, a mechanical watch has a lot of resale value, it is an asset. A quartz watch on the other hand features electronic circuitry that has a limited lifespan.
Bottom line — for just accuracy, go for a quartz, for quality, class, precision and historic value, go for a mechanical watch! And for some of you, who cannot decide, buy what you like to wear!