= Solution
The relevant resolution condition is on the <oscillation phase>, not solely on which <mixing angle> is being measured. Since $\Delta\propto L/E$,
$$
\sigma_\Delta\simeq|\Delta|\frac{\sigma_E}{E}.
$$
At the same medium baseline, the fast $\theta_{13}$-dependent ripples have phases about $37.5$ times larger than the slow $\theta_{12}$ component. Resolving those ripples therefore requires a much better fractional <energy resolution>. At 47 km, $|\Delta_{23}|\simeq59.5$; avoiding substantial phase smearing requires a resolution appreciably better than $1/59.5\simeq1.7\%$.
However, a short-baseline $\theta_{13}$ experiment near 1.24 km and a $\theta_{12}$ experiment near 46.5 km each operate near their relevant first maximum, $\Delta\simeq\pi/2$. Their intrinsic fractional phase-resolution requirements are then comparable. The smaller $\theta_{13}$ disappearance amplitude demands careful relative calibration and background control, but it does not by itself impose a universally finer <energy resolution>. The proposal is conditional on baseline and analysis, rather than a general requirement.
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