In comparing the best way to utilize our savings vs chequing account the best approach would be

To keep all of our money in our chequing account as that is the most liquid, leaving our savings as a back-up 

To keep enough money in our chequing to cover our monthly expenses, while moving excess savings to our savings account to build up an emergency fund 

To move all our money to our savings account, because unlike our chequing it can't be used to tap and pay and that inconvenience will help us save 

To split every dollar we earn between our chequing and savings account, regardless of other financial factors, because that best takes advantage of both accounts.