Mapping Center Answer:

Well, in over 15 years of being a geographer and cartographer, I've never been asked to express a coastline in terms of length.  I'm therefore fearfully full of curiosity wondering why that would be relevant?

To get to the question though, units has little to do with it, though I think I understand what you're really asking.  If the coastline were measured in feet, would it be longer than if in miles.  Only if you were relegated to using integer values, and if you rounded the miles down. 

The real issue is what is the minimum mapping unit, i.e., the length of the shortest line segment one would digitize or extract from an elevation dataset to represent a portion of a coastline with.  The smaller the minimum mapping unit, the more detail can be captured, and therefore the tendency is to have a longer line.  That said, the more detail one adds, the more features like small coastal islands, rocks, and such creep into the work, along with whether the tide is in or out, and soon you find out why mapping coastlines is a really tough job.  Either way, I would not use line length as a determinant of quality, in any unit. 

I don't know of any standard, but NOAA would be the U.S. Agency to check that out with.