Which type of bond is stronger, ionic or covalent?
However, we are comparing apples to oranges. Ionic bonding is a non-molecular interaction, in which every cation, every metal ion, is electrostatically bound to every other anion in the lattice. And a covalent bond (in its simplest form) is a region of high electron density between 2 positively charged nuclei such that internuclear repulsion is negated and a net attractive force results.
Note that covalent bonding can also be non-molecular. The lattice structure of diamond or silicon dioxide features strong covalent bonds which persist across the entire crystalline lattice. As a result, the melting points of diamond or graphite, are so high as to be almost unmeasurable.
I do realize that I have not answered your question.
It is a bit of a toss-up, as stronger and weaker cases are found for both types.
As the preceding answers have stated, these are two quite different types of bond, and within each group, you find a range of strengths. So, I do not think it is possible to assign a strength to either ionic or covalent bonding as a group.
That said, the hardest substances known, diamond and quartz both are network solids held together by covalent bonds. So, if I had to make a choice, I would go with covalent bonds.
By the way, when we look at the melting points of substances that show covalent bonding, it is not the strength of the covalent bond that is being tested. The covalent bonds hold the toms together within the molecule, leaving much weaker dipole forces or dispersion forces like van der Waals forces to hold molecules in place in the solid. What I am saying is, that you must not use melting and boiling points as a means of indicating covalent bond strength in these molecular compounds.