Having a larger account balance affords you more buying power without the need for more leverage, meaning less risk. This is indisputable, regardless of whether or not the draw-down is the same between the small and large accounts.
Keep in mind that the argument that you initially posed here is that there is no benefit to traders to make use of such programs over trading that same capital on a personal account.
We have to consider not only risk, but account growth and profit-potential over a given period of time, as well as technical factors where leverage and margin calls/stops come into play.
Then you have broker offerings/conditions to consider, as well as overall financial security that one might not be afforded if trading on a personal account via an offshore broker that operates outside of the legal jurisdiction of wherever you reside. Trading with a prop firm that is local to US/Canada adds an additional layer of protection, while also providing possible access to otherwise restricted brokerages.