Do we know that what the chemical mechanism for damage from charged particle beams is? Is it similar enough to compare directly like this? Are the timescales short enough that charge deposition might matter?
So it's clear there is a temporal FLASH effect, which is not purely a question of radiation type.
That's not to say it's necessarily exactly the same effect - we still don't have a perfect quantitative understanding of the effects of different radiation types even at normal dose rates, let alone when FLASH differences are added into the mix.