But 'lower' in what specific way is the question.
I would say that any answer I give you will be open to conjecture by many who would just want to argue. What I can say for certain:
I have shot 1000's of rounds of HST in 9mm and 45, not so much for the Punch line, as I just recently heard about it, but I did purchase some in 45ACP recently, just to see if my gun liked it, and if the point of impact/grouping was any different, at 25 yards. It was not.
I did not chronograph (as I think this is dumb when it comes to a real pistol)
But subjectively, I found no difference in how the round shot, and impacted the steel target.
Physically, the HST has a nickel plated case, where the punch did not. I could see it being a nice feature for LE officers for durability, or for CC use, as the nickel would be nearly impervious to sweat and corrosion.
I suppose you are looking to purchase one or the other. I would not recommend one over the other, unless the nickel plated case would be more suitable for your needs as stated above.
If it was me, I would just stay with the HST, which I carry in my 45. Two mags of HST are with the gun when I carry it.