Recording activities - case or contact summary page?
Kate, Welcome to CiviCRM stack exchange. About your question, it depends upon your business logic. If you want the activity to be part of the case than you should create them inside a case since the New Activity form from the Contact summary page doesn't provide ability to add activity to case. You can but obvious move the activity later after creating by using Move to case link or Move to case from task action. 

If you don't want activity to be part of the case than you should use option from Contact Summary screen. 

Thanks

Pradeep