use your smartphone for time of day precision. it's the most accurate as it relies on precision time protocol synchronization on the network with constant augmentation and calibration by gps or glonass and or a grandmaster (atomic) clock that has either a rubidium or cesium source. those sources are down to within 10ns in clocking or time-stamping precision.
No question about precision when it comes to the smartphone or even atomic-synchronized watches (not avail in S'pore).
But there's something organically, viscerally, primordially satisfying about keeping time simply by the movement of your hands using mechanical tools – your body is the sole source of power, no external solar or battery source needed, no electricity generated, no motor used.
And a good mechanical watch today keeps time to day to within 5 seconds a day, good enough for most. Do you need to live life to a precision of 10 ns a day? Is it even possible, given that most human-scale events occur on a scale of minutes and hours at the very most precise (no one specifies a meeting at 8.01 & 53 seconds am!)?
From a functional point of view, if your life depended on your watch – climbing Mt Everest, exploring the Antarctic, exploring Guilin caves, would you want a device where the battery could suddenly die on you, or the solar cell stop functioning because there's no sun, or the atomic synchronization fail because of an unavailable signal?