The answer also depends on how you define "break the bond." Typically, for covalent bonds, you are talking about homolytic cleavage (no charges produced), in which (for example) gaseous H-Cl becomes gaseous H and gaseous Cl (103 kcal/mol), or gaseous H₃C-H becomes gaseous H₃C and gaseous H (99 kcal/mol). If we define "breaking" an ionic bond the same way--so that, for example, gaseous NaCl becomes gaseous Na and gaseous Cl--the number is 99 kcal/mol, different than for HCl, or for that matter different than for CsCl (105 kcal/mol).

You can find some of the numbers needed to calculate what I'm talking about at the NIST Chemistry WebBook.

The only way your question could be answered in the abstract would be if we had an example of a substance that could exist as either an ionic or a covalent compound. And of course we don't, because for each compound a different arrangement of ionic/covalent interactions gives the lowest overall energy, and changing that arrangement will give you some other compound. For example, you can't compare ionic SiF₄ with covalent SiF₄! Silicon tetrafluoride is a covalent, gaseous compound with a rather strong bond (Si-F is about 140 kcal/mol).