I remembered the Major as shooting a REAL Lefever too . . . but I could well be misremembering. At any rate, I outrank him, so I MUST be right!

Further price comparison, 1936 A&F catalog, both the "basic" gun (DT/extractor). Ithaca Field, $43. Fox Sterlingworth, $42.85. Those guns were really priced competitively back then.
I've owned both. Currently have a Sterly 20ga ejector gun, weighs less than 6#. You will not find a NID 20ga that light. Both guns saw various "tweaking" to the design as time went on. IMO, the NID tweaks resulted in a nicer-looking gun with cleaner lines. (Lost the cocking indicators, stippling on the fences--and it's the version Steve Lamboy chose as the model for his Ithaca Classic Doubles.) Meanwhile, the late Sterlingworths got an uglier (IMO) blunt-nosed forend, lost the PG cap.
So for me, it comes down to when the gun was made. If you're talking 1926, Foxes still made in Philly, NID's with the snail's ears cocking indicators, I'll take the Sterlingworth. If you're talking 1938 Savage Sterly vs the last version of the NID, my vote goes to Ithaca. And, as Mark pointed out, on the used market you'll get a NID in much better condition than a Sterly for the same money.