Talking of 'break in periods' can be a bit risky. There are two camps on this. One believes that the oils and mechanisms inside an auto watch need some time to bed-in, improve viscosity, 'mesh' perfectly and the like. Others believe that a watch leaves the factory in as good a condition as it can be (other than regulating for accuracy perhaps), and from then on it will only wear out, deteriorate etc.
Some watches will improve their accuracy over time, others won't. I don't think there's a science to it, just anecdotal evidence of different experiences for different owners.
If you're concerned about a 16 sec time loss per day (which does seem to be on the high side), try taking it to a watchmaker for regulation. I don't know if you should wait for a period to see if it improves - it certainly doesn't cost anything to wait so I personally would probably give it a month or two of regular wear before deciding what to do with it.
Best of luck (and have we seen any pics of the new watch here?)