Just thought of another huge factor that impacts HPverse negatively.

By virtue of getting to 20th level, a wizard is an expert in a whole bunch of fields - a very conservative estimate of of 20 Intelligence gives him 7 skills to train, and even discounting one for Concentration that's six very broad fields of Knowledge in which he is a super-genius that is capable of discovering previously unknown things just by pausing to think.

Compared to that, HP wizards are utterly ignorant of everything that isn't connected to magic, because their education doesn't feature things like military history and tactics (how many wizarding wars have there been, anyway?), administration, mathematics, artifice (even wandcrafting is more of an art than a science), and so on. And their spellcasting isn't based on intelligence either, so there's no guarantee that a powerful wizard will be especially smart or wise. Even if their magics were comparable enough to have a drawn-out war, Tippyverse would win though superior strategy and logistics.