Thats not wrong, but not entirely accurate, the bullet diameter is similar, but the casing size on the 30-06 is much larger and able to hold much more powered, thus giving a much higher muzzle energy. So it should do even more damage. But it also depends on the type of bullet used. FMJ vs jacked hole point vs plain soft lead.

https://www.foundryoutdoors.com/blogs/caliber-ballistics-comparison/30-06-springfield-vs-7-62x39mm-ammo-comparison-ballistics-info-chart