Use of std::sort(vec.begin(), vec.end()) depends only on the operator< function. It does not require that the function be able to work with const objects.
std::greater, on the other hand, requires the function be able to work with const objects.
You will see a similar problem if you use std::less, such as std::sort(vec.begin(), vec.end(), std::less<MyStruct>()).
Having said that, there is no reason for the operator< function and the operator> function to be non-const member functions. Any member function that does not modify member data should be made a const member function.
