I can't tell the difference unless it's a high accuracy movement. Whatever minor variations in accuracy I experience between battery-powered quartz, eco drive, Swiss, Japanese....the only way I would ever notice the difference would be on the rare occasions I hack quartz watches to the atomic clock. I might do that a couple of times a year and don't keep track. I have one relatively inexpensive ETA high accuracy quartz movement that's supposedly accurate to within 10 seconds annually. It's running pretty close to that - a stitch slower as the weather heats up, but it might start moving a little faster in the fall. last time I checked, it had gained five or six seconds in five months. For a sub-$500 watch, that's quite good.
I have a few watches that have high torque quartz movements, Seiko Tuna and Marathon JSAR. I think that has more to do with the strength of the motor than accuracy.
The only quartz movements I've worn that failed were Seiko solar - one purchased used so I don't know how it was treated, the other a Prospex solar diver our son kept in a drawer for 3-4 years. Replacing the rechargeable battery on our son's watch didn't fix it, and he didn't want to pay to service it; I replaced the solar movement on the used watch, around $120, and it was money well-spent - it runs fine now.