I've owned both, but it's been a lot of years. I only owned one Hercules but multiple Nitro specials. But given that Iver Johnson and Ithaca were competing for the same market with the Hercules and the Nitro Special, I'd be surprised to learn that Hercules barrels were used on Nitro Specials.

I have a reproduction of Stoeger's 1940 Shooters Bible which shows just how competitive the market for "second tier" sxs was back then:
Hercules with extractors: $35.20
Winchester Model 24: $29.72
Hunter Fulton: $ 29.95
Fox Model B: 26.00

The Nitro Special wasn't included in that book.
The Hercules has a bit of an edge on the others (IMO)in terms of fit and finish. Fox was dropping the Sterlingworth that year and replacing with the much less expensive Fox Model B (Actually made by Stevens.)
$5 meant a lot as America was recovering from the Depression and about to find itself involved in WWII.