Generally, I've found most of the two cent pieces I've run across tend to be reasonably well struck. Others may vary.
Weak strikes are very common on early coppers. 1852 and 1853 are notorious, especially for a weak periphery. The cause was improper strike pressure and probably improper basining of the dies. Can't help on the N variety, I sold my Grellman and Reiver many years ago when I stopped doing Late Dates. IF you're really into LD's, you should get a copy.