EBS (Elastic Block Store) means that there is an abstraction of a hard drive available for the root of your instance. If your instance terminates then everything is still there.
If you use the instance store then the contents of your root directory are stored in the image on S3. This means that, if the instance terminates, then all the information in the root directory goes away.
I've been using a (now very old) Ubuntu instance using the instance store and it's not a problem. The data I really want to persist through reboots is stored on EBS volumes which are mounted into root (in this case, this is database data and app server applications and logs).
The issue becomes what happens if you need two of the same instance and need your pool of instances to grow and shrink based on demand. If you were using an EBS root store then you would need to copy the EBS data before starting the second instance. With an instance root store you can just start it.