Case classes can have methods on them, for one - I can see how that might be added to yours, but it'd probably be very awkward syntactically if you wanted different methods on different cases. To me, it also feels like your enum class is more of a special case. Scala's case classes and sealed traits work together as independent features that come together to provide value. I've used case classes before without using the 'enum-like' property of sealed traits, where I just want to get equality, unapplying, etc... for free.

They also have more configurability - while a case class provides default implementations for things like equality, you can override those (this could be a pro or a con depending on whether you prefer flexibiltiy or performance, I guess - although arguably the flexibility should only have cost if you use it, assuming it's implemented well).

It's definitely not a huge difference, and arguably Scala can suffer from it's philosophy of providing tools that can do something rather than tools for something that means the language often comes across as huge and as having too much stuff in it. I like it, but it's not the C# way right now for sure.