It's an issue of intensity, not of brightness.
Where did you learn that?
What's the difference between brightness and intensity?
BTW: it's not brightness or intensity. Brightness is not an SI unit so that's ambiguous. It's about irradiance or more specifically PPFD (e.g. µmols/m²/s) or how many photons reach the leaves of the plant.
It not about HPS vs. LED. It about growers not understanding LEDs. they replace their HPS with some shitty Chinese fixture where the seller lies about how it's irradiance is equivalent to the flux of some HPS lamp. Which is total bullshit but no one seems to understand watts and irradiance.
More likely the difference will be found in terpenes/terpenoids, phenylpropanoids, and fatty-acid- derived volatile molecules. Combinations of the various wavebands in the incident light mixture effect plant growth, development, metabolism, and morphology. (Folta K., Carvalho S. (2015). Photoreceptors and control of horticultural plant traits. HortScience)
But seriously, where did you learn:
It's an issue of intensity, not of brightness
Citations are always a nice thing to back up what you say.