Which have higher melting points ionic or metallic compounds?
This is a hard question to answer. I propose that ionic compounds (in general) have the higher melting points.
Most metals have melting points that are accessible in a laboratory or at least in a forge or metal foundry. A few metals are even liquid at room temperature. Caesium is one; can you think of others?
Both metals and ionic solids are non-molecular materials, that are held together by strong electrostatic forces. Because metallic bonding is rather fluid, i.e. bonding results from the delocalization of valence electrons across the metallic lattice, metals tend to have lower melting points. Certainly, metals are malleable and ductile, and are good conductors of heat and electricity, whereas ionic solids are frangible and non-conductive, and again this is another consequence of metallic bonding versus ionic bonding.
On the other hand, ionic bonding depends on a rigid crystalline lattice of positive and negative ions; with each ion electrostatically bound to every other counter-ion in the lattice, and electrostatically repelled by every other ion of the same charge. There is demonstrably a net attractive force that binds the solid together.
Anyway, as a chemist, as a physical scientist, your argument should be informed by numerical data. Find the melting points of a few common ionic solids,