I would generally detect any new park, school, etc. with the stock coil first. While doing that, I can identify areas that have multiple targets in every swing, such as around the pavillions and picnic areas. Then, if I think there are good targets in those areas, I go back over those areas slowly with the sniper coil. It is especially rewarding to find something good-like a silver dime-right between some pulltabs that were obscuring the "good" signal.
There are other reasons to use a small "sniper" coil. They are smaller, and lighter weight. This gives you 2 advantages: they fit in smaller spaces, and they are easier to swing for longer periods of time.
Snipers are also a little less powerful/sensitive. If you are trying to reach maximum depth, this may be a disadvantage. However, this coil property can be used to your advantage too. They are less susceptible to interference from EMI, or metal structures you want to detect close to. Also, with your detector's sensitivity adjustment turned down, they can be tuned to ignore most targets, so you only hear the surface or very shallow coins...or whatever.
Yet another positive note for the sniper coil: more accurate pinpointing!
I have read that the ID numbers are more accurate with a smaller coil, too, but I haven't payed close attention to that yet.