Hypothesis: The difference in feeling that some people get from fonts is like the difference in feeling many people get when they pay a lot for the wine they drink. It's subconscious. It feels like a real feeling. It just isn't driven by the actual experience of the product.
In the wine world, it is possible to isolate this effect using blind taste tests. In the font world, there seems to be no robust way to show a font expert Helvetica without letting them recognize that it's Helvetica.
I don't think that analogy stands. You can tell there's something different between them, specially on a full page of text, without knowing what typeface it is at all. Helvetica is slightly more elegant. That said, it is no surprise that it's hard to tell the difference since one is a rip-off of the other.
Or like Stradivarius in classical music. There have been blind tests when a contemporary violin was mistaken for the Strad. Yet classical musicians still covet the Strad - my theory being that it makes people listen with this subconscious effect you've been talking about. Same sound, but if we believe it comes from a Strad, it seems better.
Does this feel different? I can see the slanted Arial terminations but I don't "feel" the different mood.