I currently use a v-cut because I like how the smoke draws out of it, it's a small, quick cut, and it doesn't ruin the cap/head. Some of the cheaper made cigars I have start to fall apart when I cut off the head using a full cut with a guillotine. I have no experience with a punch cutter. What do you like best and why?
This is the portion I honed in on. You might be cutting them too far past the cap. Fwiw, you don't need to cut more than say, half a centimeter off. Back when I first started this hobby, a great man and good friend Brian (Infinity) showed me how to properly cut a cigar with a guillotine cutter. For a beginner or to get a better idea of what I'm talking about, place your cutter on the top of the cigar, flip it over until the cigar head rests on whatever surface you've placed below it and with the cutter resting on the table, gently apply pressure to the guillotine cutter and rotate the cigar. What *should* happen is that you will shear off just the cap of the cigar, a very small piece.
Remember, the deeper you cut, you have more chances of unraveling your smoke from cutting too far down.
To answer your question, I use my Palio cutter regularly but sometimes I branch off onto using my Opus X V Cutter. Works like a charm.
Hope this helps.