Fine threads are easier to tap into harder materials and thin-walled structures. They have bigger tensile stress areas which can make them more resistant to tension than coarse threads. Finer threads also have greater minor diameters, providing higher shear strength.
Coarse threads are recommended for more brittle materials and are less likely than fine threads to cross-thread. Coarse threads are better suited for thicker coatings and plating and last longer without thread adjustments needing to be made. Coarse threads are also more tolerant of harsher work environments and disassemble quickly and easily.