While a mechanical timepiece will never be as accurate as a battery-operated quartz watch, excellent accuracy can be obtained from a quality spring powered timepiece (depending on the quality of the movement of course).
In general, a high-grade watch will keep time within a few seconds a day. A medium grade watch will vary up to 20 seconds a day. A low-grade watch may lose/gain several minutes a day. Many factors affect the quality of a watch, but the jewel count of a typical American made watch will usually be a good indicator of quality. Higher quality watches tend to have up to 23 jewels, medium 15-17 jewels. A watch with 7 jewels is considered average, and anything under 7 jewels is typical of a poor timekeeper. Also, older watches with older cylinder escapements and “dollar” watches with pin/pallet escapement will not be very reliable. (These numbers are for time only watches…watches with complications such as calendars and automatic winding will have a higher jewel count)
There are other factors to be considered, including temperature, and isochronism (the ability to keep constant time throughout the wind cycle of the mainspring). The higher quality of the watch, the better it can be adjusted for these variables.
Precision also depends on how the watch is worn (sometimes called a personal error). For example, a pocket watch that is laying on your nightstand most of the time will run at a different rate than if you use it every day (i.e. On its back or ‘dial-up’ during the night, and ‘pendant up’ in your pocket most of the day). The same type of rate variation is observed for a wristwatch, although the positions are a bit different. While some variation in rate may be observed over short periods, this is often smoothed out over 24 hours as the watch is moved between positions. Here again, the higher quality the watch, the easier it is to adjust for positions. High-grade watches will not vary more than 10 seconds or so between 5 to 6 positions, while the 7 jeweled watches typically will vary up to 1 minute between the stem up and dial-up positions.
And any watch that is not maintained well will lose its accuracy over the years. And of course, as the bearing surfaces wear (worn jewels and pivots, and gear teeth), then the accuracy will also worsen as the piece ages. However, I have seen high grade watches over 150 years old still keeping excellent time if they have been maintained well.