My guess: If the active diode structure is the same (composition, size), it would be the same brightness. What would be different are thermal properties, what are mainly related to the substrate (as it is the biggest amount of material in the complete die). What is important there is thermal conductivity of the substrate, gives the Rth(Junction-Case) and it's thermal expansion compare the expansion of the main LED material (may limit the operating temperature due to mechanical stress). So what may be different is the power dissipation handling capability.
But it does not have to mean, then the more expensive LED uses the material with better property. As with the better material the die may be more loaded (per unity area), it may be smaller for the same rating and (in case the die cost is dominant) the smaller die would result into cheaper product. But in such case the smaller die would yield less light for the same current, simply because of higher unity load of the junction (LED's reduce their efficacy at higher load - all mechanisms are not known yet, but it was found, then the temperature is not the dominant one here)
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