Enums vs inheritance isn't straightforward. Enums make it easy to add new kinds, while inheritance makes it easy to add new methods. They are more extensible in different directions. If it's very rare for you to add new values to your enum, and more frequent for you to switch on that enum, prefer enums (and always throw in your default clause!). If you are adding enum values all the time, and only have a couple of methods that switch on them, then prefer inheritance. Although if you're using Java, consider methods on your enum values instead.
To understand the enum / inheritance tradeoff better, examine the Expression problem: https://en.wikipedia.org/wiki/Expression_problem