Wow. What a match up. I suspect this has been done many times, but I can't recall seeing it before. Pep is my #1 FW of all time & Armstong my #10, but that's only based on fights in & around FW. My gut feel is that this would come down to how strong/fit a peak Armstrong was at 126lbs. I don't think Pep could keep the 133.5lbs Armstrong, that dominated & scored multiple KD's against the great Barney Ross, off of him. The fact that Armstrong weighed 2lbs inside the FW limit vs Petey Sarron suggests he wasn't desperately struggling to make the weight, but with Pep's elusiveness the fight is likely to last much longer than the 6-rounds Sarron went, and if a fighter is weakened at the weight, it's the later rounds when it's likely to tell. If you allow me to give a caveat to my pick, it's Armstrong close UD, provided the Sarron version is strong enough at the weight to fight at his legendary pace for all 15-rounds. Gun to my head, and I'll go with that outcome, with Armstrong overturning around an early points deficiet to win a close decision, despite landing clean with an unprecedentedly low % of his punches, because Pep can't get set often enough to throw enough punches to win many rounds after the first 5 or 6.
The ultimate swarmer vs out-boxer styles match up. As great and slick of a boxer Pep was he'll be in the trenches with Armstrong 's constant pressure and won't be able to consistently escap from his onslaught. Armstrong outpoints Pep in a great fight.
The problem Pep would have against a fighter like Armstrong is he didn't have the firepower to keep Armstrong off of him, keep him honest, this fact would allow Armstrong to eventually walk him down In a 10 rd fight, Pep probably wins, but in a 12 rd, and especially a 15rd, Armstrong's perpetual attack would allow him to close the distance around 7-8th rd, win the remaining rds , win a close decision.