The performance of the IS test in .NET is rarely a performance problem - worst case is when the result is False and the object has a deep inheritance hierarchy. IS will have to perform multiple lookups going up the object's inheritance chain.
Unless your objects all have deep (100+) inheritance, the performance difference will be negligible.
The biggest difference between testing inheritance and testing an enum is that you can test an enum against multiple values in a switch statement. IS tests always require an if statement chain. The larger (> 10?) the number of elements to test, the greater the performance advantage of switch statements over if statements.
Creating a design where testing the type of the object is a key element of the design seems highly questionable. You should be trying to use polymorphism to allow you to manipulate various types without needing to know the type of each object. A virtual method call will be faster than testing inheritance or testing enums when the number of types involved is greater than 1.