6.5 Grendel VS 300 AAC?

[JASmith]

...why or "how" is it an improvement over the 7.62x39?

One, and a major reason the 5.56 is so entrenched, is the number of rounds available in the magazine. The 300 AAC is essentially a necked-up 5.56 so the cartridge base diameter is appreciably smaller than that of the 7.62X39.

So, the improvement is "getting the same performance in a smaller package." For locales where 5 rounds is the largest magazine permitted, there is no practical difference. When that limit is not present, as in LE, military, etc. the larger number of rounds can make a difference.