RBAC is the bigger brother of accessRules(), in the family of Yii authorization methods. It is more robust, powerful and usually employed in more complex use cases, but this depends on your requirements and tendencies.
When you use RBAC, you do not need to (and be better off without) check permissions using Yii's accessRules() which is using a predefined Yii filter. Be sure not to miss that defining the method accessRules(), you also need to tell Yii to use filter 'accessControl' on the action methods. So in short - don't use both. Lose both the filters directive (or the entire methods, if you have no other filters defined) and the 'accessRules()' methods.
By default, RBAC will consult regarding the 'auth items' hierarchy and the auth items assigned to users in the DB. You can manage the DB by yourself but I strongly recommend you consider using several ready made extensions for managing (only) the 3 tables of RBAC. For example, RBAM and SRBAC. Both are not bug free , but reduce lots of work, in case you have a more than trivial permission's tree.
Last but not least, be sure to read the relevant page in the guide.