is this statement true?
More heat is needed for vaporization of a liquid compared with melting a solid of the same substance.
That certainly is true for water. What about other substances? Here is a table for heats of fusion and heats of vaporization. Compare them and see.
http://chempaths.chemeddl.org/services/chempaths/?q=book/Quick%20Resources/1251/table-molar-enthalpies-fusion-and-vaporization