This is just my experience, and I seem to be a bit of a freak when it comes to quick labours

DS was induced as my waters broke and I was GBS positive and contractions were slow to start. I was induced at 8pm, full labour was established at 9pm, and DS was born at 1112pm- so a 2hr12 minute labour to birth

With DD, my waters broke at 350pm, I had 10 min contractions until about 450pm, we arrived at the hospital just after 5pm at which time my contractions were right on top of each other and she was crowning, she was born at 515pm, so from waters breaking to birth there was 1hr25mins

Like I said, this is at the extreme end of quick labours (My Mum was similar), but in my own experience, yes, the 2nd labour was quicker, and my obstetrician expected it to be and told me to head to the hospital either when my waters broke or when I was contracting at 10 min intervals