The "machine gun steel" isn't so much, it's the cold hammer forging requirement that has to be met. Once done, all barrels are about the same, and dead soft annealed to prevent them losing temper. Nobody much heat treats a barrel for strength if it can be mag dumped to over 700 degrees - it will lose temper and if that strength was necessary, it could fail.
Therefore, barrel steel is mostly selected for it's machining or fabrication qualities. Like "surgical steel" knife blades, it's mostly marketing hype. With over a dozen stainless grades in knives, there is a significant difference in performance. With a barrel, it's all about rifling, harmonics, and if chromed, how much deviation in parallel is created.
In the steel alloy ranges, gun barrel steels make lousy knives. And, vice versa. You get nothing extra in a gun out of a high alloy knife steel for all the extra expense and work.
The cold hammer forged is more important. It results in smoother rifling and less deviation from parallel. That is why they are more accurate, not the steel.