Coffee can be bought either as whole beans or as coarsely or finely grounded coffee.
What are the pros and cons of the coarse and fine coffee ground? Are there different applications for coarsely and finely grounded coffee?
Mainly the grind types have to do with how long the grounds are going to be in contact with the water during the brewing of the coffee. Finer grinds for espresso (quick brewing) and medium grinds for drip, etc. This chart will give you an idea of what grinds go with which preparations http://www.ineedcoffee.com/03/coffeegrind/
There are necessarily pros and cons of different types of grinds as much as different purposes associated with different types of grinds. The coarseness of the grind will determine what type of brewing method that will be used. The difference in grind will also determine the length of the brewing process.
Also grind coffee just before brewing for the freshest cup of coffee possible. Normal grinders with blades work ok, but burr grinders work best. Regular grinders chop more than grind.
Here is an article that outlines different grinds and what brewing process to use.
if you want your grinds to have a good-decent flavor(in my experience) get a bag that has a one-way air valve (much like a respirator with no intake) thebeanforge.com sells their ground coffee in such bags. To answer your direct question, I would only assume the courser grains will keep the flavor longer than the finer grains. Finer grains may be able to bleed the flavor at a lower temperature=less brewing time. In my experience you can brew course grains satisfactorily in a regular drip coffee maker, such as the "Mr. Coffee" makers and a run-of-the-mill paper filter.