According to the Canada Revenue Agency (CRA), the person who is primarily responsible for the care and upbringing of the child should apply for the Canada Child Benefit (CCB). That person is responsible for things such as:
supervising the child’s daily activities and needs
making sure the child’s medical needs are met
arranging for child care when necessary
NOTE: The CCB is calculated according to the family income, therefore, there will not be a difference in the amount if the other spouse claims it. If you both equally care for the child, you will need to decide together who will be claiming it.