The more complications you add to a watch the more you interfere with accuracy. If you go to
www.casio.com you'll see some of their watches are specified within 15 seconds per month, others 30 seconds per month -- the difference is how many complications they have.
Quartz watches are affected by temperature a little, but the main factor other than complications is how accurately the quartz tuning fork is cut in the first place. Simple quartz watches have a very consistent rate of going, but exactly what rate is a matter of chance, within spec. They cut the crystal with a laser and then test it long enough to see that 95% or so are within spec. There are a few (expensive) quartz watches on the market with high-beat crystals and/or temperature compensation for greater accuracy, but the usual design has a crystal that beats at 32K (32768). In an analog watch that 32K is divided in half 15 times by a 15 gate counter circuit to produce one pulse per second, which runs a stepper motor that makes a 180 degree turn with each pulse.... Whatever brand you buy at whatever price, except for those few expensive watches that use a different design they're all the same and the accuracy you get is a matter of chance. It might be within one second a month if you're lucky or it might be twenty seconds a month off -- and the odds are the same whether it's a relatively expensive watch or a cheap one. There's very little motivation to improve accuracy because most people are satisfied with any quartz movement; the few fanatics like me who want better are a small market.
It has sometimes occurred to me a cheaper way to get a very accurate watch than to buy one of the better designs would be to buy about a dozen quartz watches when there's a sale at a discount store -- sometimes you can get pretty decent watches <$5 -- test them all and pick the most accurate one. YOu could give the others away for Christmas presents; most people don't care about accuracy....
The clock in your computer is quartz-controlled but that crystal is running a lot of other stuff too; that's why they're so inaccurate. There's a variety of software on the market to set it -- I've been using NetTime, which pings back and forth with all 144 different time servers to determine the lag and the variation in the lag, picks the best five or six of the bunch, and averages them. It's typically within <500 nanoseconds.
I can't say NetTime is the best, though -- there are about 50 or so different programs available and I've only tried a few of them. NetTime is free.
Time Synchronization Software