What type of compound usually has higher melting points: ionic compounds or covalent compounds?

The ionic bond is stronger than the covalent bond so it takes more energy (heat) to make the ions come apart. When they do come apart and melt, one atom will still be more positive and the other more negative. In a covalent bond the atoms share the electrons and neither atom has to give up its electron completely. In an ionic compound like salt (NaCl) sodium gives up one electron which goes to join with the chlorine atom. So you have  positive sodium atoms and a negative chlorine atoms in a nicely organized array which is the salt crystal.

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