The 3 in was an adaptation of a 3" coast defence gun that dated to before WW I. It had the advantage of being available in the sense that blueprints existed, production tooling may have existed. The internal Ballistics were understood and the method of manufacturing the barrel was understood (and common).
The 76mm M1 had the same exterior ballistics/performance (same velocity with the same weight shot) but used a smaller cartridge case at much higher pressure and a different propellent.
The Gun itself used different steel and a different method of construction/fabrication that allowed the barrel to be much skinner and lighter.