Which are stronger bonds, ionic bonds or intermolecular forces? Which have higher melting points, ionic compounds or molecular compounds?

Ionic compounds are inherently non-molecular. Each cation is electrostatically ATTRACTED to EVERY other anion in the crystal. Of course, each cation is electrostatically REPELLED by EVERY other cation in the crystal, but if you sum up the attractive versus repulsive interactions, which can certainly be done quantitatively, a net attractive force result.

Molecular compounds generally have indifferent forces of attraction BETWEEN molecules. And thus, lower temperatures are all that is necessary to disrupt the intermolecular interaction, and melt (or boil) the bulk material.

Molecularity is a very important concept to apply in this context. Carbon as diamond and graphite is non-molecular, with no molecular boundaries, and thus unfeasibly high melting and boiling points. On the other hand methane, whose #C-H# bonds are certainly stronger than #C-C# bonds, is a room temperature gas, precisely because this is a molecular material consisting of discrete molecules of #CH_4#, which are bound together by weak dispersion forces.