Could you explain me what's the difference between those two things according to you?
Sure. The thing to keep in mind is that K-Weighted loudness curves exist to normalize how humans
perceive volume; these are f.ex. used on TV and radio to process audio so everything
sounds more or less the same volume across the frequency spectrum.
The issue with using loudness-adjusted measurements for accuracy testing is that how humans perceive things has
little to do with how similar two audio signals are. As you mentioned, LUFS highly favors the mid- and high-end, so low-end inaccuracies will have little impact on the resulting measurement, even though those differences will be completely audible.
But wait, we listen to signals with our ears, right? Problem is, the fact that humans perceive bass as less loud than treble at a given level doesn't mean bass goes away entirely. The bass region for two different profilers could measure the exact same in LUFS, yet sound wildly different.
As i said, using LUFS is a good starting point, but reducing modelers comparisons to it is a very flawed approach IMHO.
I'm curious to hear that now...
Just do a quick search on his YouTube channel

I like how Leo bothers to include these clips in his shootouts.