Instances with mounted EBS volumes are like virtual systems connected with virtual hard disks. In most of the cases, having this hard disk for your system is more preferable than just your system's internal memory, that is, in AWS terminology, the instance store.
Pros of EBS backed instances
EBS volumes are instance independent so if the instances get terminated, your data won't be lost.
You can stop and start your EBS backed instances without losing any data on your EBS volume.
You can dynamically modify the size the EBS volume
You can mount an EBS volume that was in use before to a brand new instance and can access the data present in it.
Pros of Instances with instance store as the root volume
Using EBS AMI can get costlier than some of the non-EBS backed AMI, so Instance store volumes are cost effective.
Instance store volumes are local so they are faster and don't need any network-based storage.
Instance store volumes are perfect for performance-critical data.