Practically you will see no difference whatsoever.
It's only in the syntax, and the ability of a constructor to perform stuff automatically, though you still have to create instances to invoke the constructor, which in this case is not far off calling some equivalent static
member function.
However, non-static
member functions are supposed to affect internal state so, if you have no state, static
member functions seem more conventional, and will be slightly less surprising to users of the class.
The best approach, though, is to stick your functions in a namespace. Classes are for data and functions operating on that data... even static
ones.