I've got a reasonable grasp of how speakers work, and have read a lot of comments that compare the tone quality of different speakers. My hunch is that two things affect punch:
1. Overall volume, which will sound more punchy but will also have more responsive feel, all other things being equal. This could be governed by sensitivity, amp power, or knob settings. It's ridiculously difficult to make all other things equal. Room acoustics will have an effect too.
2. Mid-bass at the expense of response at the lowest frequencies. This also compensates for drivers with limited excursion.
An amusing thing I've noticed is that most of the terms used to describe bass amp sound seem related to feelings of masculinity: Heft, girth, punch, slam, wham, thank-you-ma'am, roundness, and so forth.
I'm surprised nobody has begun to use the term "torque."
Marketing departments, take note.