Just looking at the vintage of the 038, I'm wondering if the carb is a pre-EPA carb. In other words, maybe some of the extra torque down low is related to the carb jetting.
A 372 is 71cc and a 038 is 72cc. Not much difference in displacement, perhaps a difference in transfer time/area is likely in the equation. However, with the Tilly and Bing carburetors on the old 038, I'm wondering, would those carbs be able to be adapted to a 372? If so, perhaps the 372 could be given a bit of grunt with an older carb.
My choice would be a 372 with a ported 77cc Big Bore and a modded carb - might as well have the best of both saws.