Yes, that is true, quartz are better at keeping time, though mechanical watches are still better at measuring time. Astronauts for example are required to use Omega Speedmaster mechanical watches on spacewalks (which at it's cheapest is still about $8000), and it was the watch used during Apollo 13 to time the engine burn (which required great accuracy).
Quartz watches "tick" only once per second. Mechanical watches move generally 6ish times a second, causing a perpetual movement. This makes them better for measuring things in fractions of seconds than a quartz movement.
If you are talking about a sweep second hand, there are plenty of quartz movements that do that.
If you go for digital quartz, you can get 1/100 second accuracy in a $10 watch.
The longer you time something, the worse the mechanical watch is going to be. Most of them gain or lose several seconds every day.
Zenith is the only manufacturer that I know does significantly better than this, but that particular movement is pretty rare and extraordinarily expensive.
