It’s generally true, yes. However there are some rare exceptions. Grand Seiko released an incredible new mechanical movement they are calling “UFA” that is accurate to +/- 3 seconds per month, and +/- 20 seconds per YEAR. That is insane.
For reference, the Swiss chronometer standard is -4 to +6 seconds per day for mechanical watches (not all Swiss watches meet this chronometer standard)
Quartz watches will typically be +/- 15-20 seconds per month.
I believe both movements have their place in a collection and use-cases. Many prefer the engineering aspect of a mechanical movement. It has a “heartbeat”. Mechanical movements are able to track the 4th dimension with nothing but gears and springs. Pretty damn cool. They are also generally more expensive to make, and a higher level of craftsmanship is required to create an accurate mechanical movement.
Additionally, mechanical watches generally have an aesthetically pleasing “sweeping” seconds hand. Quartz watches generally have a “ticking” seconds hand. Many prefer the smooth motion of the sweeping automatic movement.
The downside of mechanical is they require either winding or movement to stay beating. Most have power reserves of at least 24 hours. A submariner has a 70 hour power reserve - meaning if you put it on your nightstand for 69 hours and picked it up, it would still be running. If you picked it up on the 71st hour, you would need to wind the watch and reset the time.
On the other hand, quartz uses batteries that last 3-5 years. You can leave it for 2 weeks on your nightstand and pick up right where it left off.
In short, the preference for mechanical lies in the refinement, engineering, and tradition of the movement type.
