Chapter Discussion Luffy left Franky, Nami and Brook alone against Big Mom

[WesMidnight]

Would he have done the same against Akainu ?

I think he'd prioritize beating Akainu to Kaido due to Ace's death but if we exclude personal drama, you need haki to effectively stall Akainu so half his crew become useless.
Also Akainu is Fleet Admiral so no reason why he can't be yonko level and have the other admirals be less imposing.

 

[MD Zolo]

Well...since Nami, Chopper and Jinbei has been able to hold their grounds against Big Mom in the past, I think Luffy feels that they can hold their grounds again.

As for Akainu comparison, I don't think it works like that. Remember, among all villains, Akainu is the only one who mentally broke him. So, obviously he would be more cautious. Nevertheless, Luffy was still fine with Zoro fighting a fellow Admiral Fujitora.

But still, at the end it doesn't matter. This is Shonen and so the MC will be made to go up against the primary villain i.e. Kaido and not secondary villain i.e. Big Mom. That's just how it is.