From my understanding, private banking gives you reduced fees, more personalized service, better rates, more investment options, more services, etc.

Regular banking nowadays often requires a monthly service fee unless you meet certain requirements (specificed average daily account balance, certain number of transactions, etc.). I'm not sure what executive banking is. I would guess it's similar to private banking which generally gives you more personalized service (dedicated rep, etc.).

Most likely your accounts either have high daily average balances (6-7 figures+) or you are doing a large number of transactions which is why they're offering you private banking. I'm not sure why you'd turn it down unless your you foresee your account amounts declining in the near future which could result in large monthly fees to maintain your private banking profile.