A quartz watch has a slight edge on shock resistance over the mechanical, but it is certainly not invulnerable. Low mass of the vital components helps protect them from shocks. Most vulnerable spots in a quartz watch are the stepper motor and the quartz crystal package. Most vulnerable in mechanical watch is the balance wheel's cap jewels, the balance staff, the rotor bearing (in an automatic) and from there, various other parts of the escapement, especially cap jewels. The case and crystal are equally vulnerable in both kinds of watches.
No contest in the low-temperature sweepstakes: A well-maintained mechanical watch will keep on ticking long after the battery of a quartz is temporarily immobilized. High temperature durability is less clear. Accuracy of both degrades rapidly at temperatures well above skin temperature.
Given everything the same, a quartz watch should be able to maintain its water-resistance better than a mechanical, simply because of its far less frequent need to have its crown unscrewed for time setting. But there are many other variables here,including the robustness of the individual watch.
Vulnerability to strong magnetic fields: A mechanical watch is generally more readily affected by a strong magnetic field, but the effect is reversible although a nuisance. Not so with the quartz: A strong enough magnetic field can depolarize or partly reorient the permanent magnets in the stepper motor. This can't be reversed.
A mechanical watch is for all practical purposes invulnerable to strong electrostatic discharges and RF electromagnetic fields. The quartz watch's CMOS logic chip and stepper drivers can be destroyed by just the right (or we should say wrong) zap. The EMP (Electromagnetic Pulse) effect associated with nuclear detonations can also be fatal to any microcircuit, but let's not worry about that - a nuke can do more to you and me than it can to your watch. In fact, it can ruin your whole day.
Resistance to mechanical wear in the movement is much better in the quartz watch because the gear train of a mechanical watch is under constant load from the mainspring. This load is particularly heavy at the mainspring barrel. Further down the line, the wear is increasingly due to friction between gear tooth surfaces and between gear staffs and their jewels. Obviously, the better maintained the watch, the less significant the wear. In a quartz watch, the gear train is under no load. For this reason, it doesn't need frequent (in some case ANY) servicing to maintain proper lubrication.
Resistance to aging is definitely far superior in the mechanical watch, providing it is well maintained and protected from mosture and chemical contaminants. There are watches today that are still running after 200 years of service. While quartz watches have not been around long enough to establish reliable longevity data, some of the mechanisms that contribute to a watch's deterioration with time are known. They are the normal aging of discrete electrical components, solder and spot-weld connections, damage from dead batteries left to deteriorate and/or leak in the watch, etc. Still, quartz watches have the potential for decent longevity. My oldest quartz watch (a Seiko) is 21 years old and is just now starting to show occasional signs of senility. My oldest mechanical watch (a Ball Official RR Standard) is 37 years old and still runs flawlessly. However, it has over the years suffered some repairable insults, like a broken balance staff. So here is a major difference: For most old quartz watches, if they suffered this level of damage, I would pitch them. Mechanical ones I would have repaired. Why? Nothing logical -- I get bored more readily with a quartz watch. Go figure.
This is hard to separate from accuracy, because the two complement each other. Here is the gist of the matter: A quartz watch can be put into a drawer, kept there 3 months, then taken out, put on the wrist and worn. It would still show the right time (unless there was a change from Standard to Daylight time or vice versa in between) and the adjustment for the date needed to account for the short months in the intervening period is very simple. Further, you can do this with 20 watches in your drawer. Any of them can be taken out at any time and worn. The minus side of that is that out of those 20 watches there will likely be at least one that needs a battery. Unlucky you if you chose that one to take on your 2-week fishing trip!
A manually wound watch can be kept going at the price of a 30-second-per-day manual winding; no need to wear it. The same goes for 20 such watches in your drawer. However, because of the relative inaccuracy of these watches compared to the quartz, you will probably have to set the watch to the right time after 3 months of disuse. We owners of such watches will argue that it doesn't take much longer to set the watch than it does to adjust the quartz above for changes in time and date.
Automatic watches can be used as above only if they are on winders. And 20 winders can be quite an outlay of cash you could use more pleasurably buying that Lange Saxonia.
The reliability of mechanical watches is legendary. This can be true of the quartz, but for one little item: Its battery. Battery life is highly unpredictable. My own record goes to a Lassale dress watch that ran on a battery (a Varta, I believe) for 7 years! But then, it ticks only once every 20 seconds, advancing 1/3 minute each time. My experience with batteries is that much depends on its age when you bought it and a variety of other factors, so you can rarely be absolutely sure when this temperamental power source will unpredictaly find itself shedding the last coulomb in its reservoir, leaving you timeless out there on the Continental Divide, where you plan to stay another week. Small wonder, then, that 'survival' watches are usually mechanical.
Replacement parts for mechanical watches are widely available, including for watches dating back to the '40s and earlier. Also, they can always be made if they are no longer available, albeit at considerable cost. Not so with quartz watch needs, particularly batteries. What about all those mercury batteries from the early days of the quartz era (e.g., the infamous 388) with their vile cargo of toxins, now outlawed? (So what if the dosage I'd get from them is negligible compared to what I get regularly at the fish market and at the sushi bar? It's the Principle of the thing!) In time, many of the batteries in common use today will no longer be available. Since it is the voltage and capacity that counts, it may be possible to use newer batteries with a suitable adapter, but if the voltage requirements are different, its Adios to that dear old Seiko or Raymond Weil your mom gave you as a graduation gift.
I won't go into this touchy subject, but you all know what I mean. I will let YOU decid which type of watch more readily falls prey to this phenomenon.