Possibly a brief undervolt condition that's not enough to trip the power supply but enough to keep VRMs from firing up properly and the chips error out because they're taking slightly too long to initialize. The 380 probably isn't nearly as busy inside as the big guys (likely active PFC and a bunch of other mess) so it might have better output capacitors since there's likely more room for them. I'd try the capacitors-wedged-in-the-6pin trick and see if that helps smooth things out.

Otherwise, really no idea why it might work on a low-end PSU but not a big sexy one.