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Covalent bonds are stronger than ionic bonds in an organic system because in an aqueous environment, the positive end of water molecules would surround the anion of an ionic compound and the negative end of water molecules would surround the cation of the ionic compound. In a vacuum however, the covalent bond would be weaker than the ionic bond.
Aside from looking at the electronegativity aspect, I think of it as how covalent bonds pretty much involve the sharing of electrons whereas ionic bonds involve the attractions of opposite charged ions which makes it much more harder to break.
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