Select an exercise in career mode, then press Left + X.
If both players have exactly the same trademark punch, player one's will be faster.
If you were wondering, the height of your boxer DOES affect his reach, allbeit only a little.
Some Trademark punches are faster than others. So if you are playing with someone and you both hit your trademark punch buttons at the same time, the faster one will hit the mark. The fastest one appears to be the "Load Up St. Right", followed by the "Angeled Left Uppercut", the "Power Uppercut", And fourthly the "Rt. or Lft Roundhouse".
If you were looking for HBO Boxing for PSX cheats, then you might also want cheats for: