Unordered sets must compensate for their O(1) average access time in several ways:
To store the same number of elements, set uses less memory than unordered set.
Lookups in a set may be faster than lookups in an unordered set for a small number of elements.
Even though unordered set is faster in the average case, set is almost always guaranteed to have lower worst-case complexities (for example insert).
If you want to access the elements in order, that set sorts them.
Different sets can be lexicographically compared using <,<=, >, and >=.
These operations do not require unordered sets to be supported.