The first interaction of radiation with tissue is usually this:
H2O + ħv >> H2O+ + e- (fugitive)
The radical ion H2O+ is extremely reactive and usually protonates another water molecule immediately:
H2O+ + H2O >> H3O+ + OH*
The hydroxyl radical has a half life of about a nanosecond and will usually be the main "reagent", diffusing until it runs into an organic molecule which will be oxidized and thus degraded. At high enough dose rates, the peak concentration of hydroxyl radicals and more stable radicals like superoxide could be much higher, leading to "nonlinear" effects, i.e. byproducts of multiple radicals interacting with each other or a protein.
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.