= Solution
Make the implicit fixed-crack-geometry assumption explicit by writing $\sigma_f=C\sqrt{EG_c}$, where $C$ is common to the compared specimens and includes the crack-size dependence needed for dimensional consistency. <linear elasticity> gives
$$
\varepsilon_f=\frac{\sigma_f}{E}=C\sqrt{\frac{G_c}{E}}.
$$
The appropriate <materials merit index> is therefore \b[$G_c/E$], or its monotonically equivalent square root. This comparison holds crack geometry and the brittle-failure model fixed; changing crack sizes or yielding before fracture changes the selection problem.
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