As for the "not keeping time" vs. "keeping time" this is because Rolex has a real clockwork and the Chanel does not. No real clockworks will keep time perfectlly, some are better tuned than others but it is more or less luck if they keep time perfectly. I have 6 Rolexes and some are better than others, but I have to adjust them monthly to be somewhat accurate.
Chanel is a Quartz movement which runs on a battery and will keep perfec time. But for anyone who is in to watches, the charm is completely gone with a quartz movement. Another thing is that a real clockwork will work for generations, a quartz movement will not. Personally, I would never even consider a quartz movement watch, even thoug I recognize that they are better at keeping time and do not stop if you stop waering it for a couple of days. I just love the thought about owing a real watch with real clockwork ticking its way on to future generations.
No Chanel also comes in automatic that is what I have. They have both styles