I don’t know where you are located. I am in the US and a co-op is just a corporation so all the things that apply to a private corporation apply to a co-op. When applying for grants there are no differentiators that I can think of. One advantage for a co-op here is that there are no passive investors.
This might be tangentially relevant https://fed.dyne.org/post/146187
Can you tell me what city this is? For me this would be reason enough to move.