Lance? I've never heard a punch cutter called a lance (I believe that is what you are referring to) ...
You need to gently twist the punch while forcing it in about a quater inch, and once you pierce the cap, the plug will come right out.
As far as which one is better? It's all a personal preference, though some larger ring sizes may need the punch unless you have a large gauge cutter (or cigar scissors) available.