I agree with everyone saying it’s personal preference and situational. For me, I only use a punch when I travel and I don’t check luggage. The reason? Even though the airlines and TSA rules do not specially ban cigar cutters, there are some TSA employees who are poorly trained or happen to have a bad attitude on the day I go through the checkpoint. Having personality experienced the ‘full TSA treatment’ when a TSA saw a wrapped protein bar in my briefcase. He decided it might be a contraband object of some sort and pulled me and my carry on stuff for ‘closer inspection.’ Since that experience, I’ve decided not to risk my good cutters (a Xikar VX2 and a SAW knife with a scissor cigar cutter. My solution, I travel with an inexpensive keychain punch. If they confiscate it I’m only out a few bucks.
The downside of a punch is when a cigar has a bad draw. With cutters, you can snip off a bit more. With a punch, they don’t always come with multiple sizes. If you only have a punch, you need to punch a second hole or you need a draw tool like the PerfecDraw. I won’t travel with a PerfecDraw either when I don’t check luggage. I figure TSA would surely have a problem with a tool that is 4 or 5 inches long, having several barbs on the point.