This whole argument seems to be framing it as "Who's better at X task?", which is obviously going to be arbitrary based on what task you pick. I think a more productive way of framing it might be "Who has more capabilities available to them?"

To put it another way, if we had to start fighting with pointy sticks for some reason (because the Gods of Anthropology demand it), we could do that easily. The technology that makes guns can easily be applied to sharpen sticks.

But if a society that only knows how to make pointy sticks has to start fighting with rifles, they're going to need a lot more effort. They need to learn the metalworking to make the gun parts and the chemistry of gunpowder to load them and the physics that shows why rifling works. They have less capability to fight with rifles. Regardless of whether fighting with rifles makes them better, the society that can fight with both sticks and rifles is more capable than the one that can only fight with sticks.

I think this might be a more productive way of phrasing "advancement." Ignore the questions of "What does this society want to do?" and focus on the technological question: "What could this society accomplish with the knowledge they have?"

Yes, there's some nuance over does theoretical knowledge count, does it count if they forgot knowledge that would help in earlier situations, etc. etc. But I think that making a definition that even vaguely approximates a layman's idea of "advanced" is better than constantly trying to explain to laymen why an atlatl should be considered equivalent to a jet fighter.