I wouldn't call the HE500 or the HEXv2 bright, as they're both on the warmer side of neutral especially with the latter's treble roll-off. None of my Hifiman cans (HE6 [prototype], Arya, HE500, and the HEXv2) are what I consider bright, especially compared to my Grado HF-3 (short listening sessions only).
Based on my cans (just my opinion):
LCD2.1 [pre-fazor] - dark
HD6XX - dark-warm
HE500/HEXv2 - warm
HE6 [prototype] - neutral (can be neutral-bright with leather pads)
Arya - neutral-bright (9-10k peak is the source of any kind of brightness with the Arya, otherwise it is smooth sounding)
Grado HF-3 - bright (to my ears)