Cutters
A cutter, be it a guillotine, double guillotine, scissor or v-cut, snips the end of the cap above the shoulder of the wrapper. However, too low a cut can allow tobacco to fall into your mouth or damage the wrapper.
Punches
A punch screws or punches a small hole in the cap. Less tobacco can fall into your mouth, and the smoke concentrates for a more full-bodied taste. However, punches are not recommended for ring sizes less than 38, and with a larger ring size, more than one hole is needed.
Availability
There are thousands of cigar cutters of all types, priced from one to hundreds of dollars, from simple to elaborate, and from pocket-sized to table style. Cigar punches are less popular, so there are fewer styles to choose from, and most are designed to fit in your pocket.
Shapes
Some cigar shapes, such as torpedo, figurado, or belicoso, have cone-shaped ends, designed to concentrate the flavor and the smoke. Using a punch on these shapes will make the cigar fall apart.
Choices
Like your choice of cigar, using a cutter or a punch is a matter of taste and preference. Just remember that biting the end off your cigar is never advised because it will damage the wrapper and the tobacco.