Statement A: The photochemical reactions ${\mathrm{H}}_2+{\mathrm{Cl}}_2\to 2\mathrm{HCl}\text{\hspace{0.17em}and\hspace{0.17em}}{\mathrm{H}}_2+{\mathrm{Br}}_2\to 2\mathrm{HBr}$ have equal quantum efficiencies.

Statement B: Both the reactions proceed by different mechanism.

${\mathrm{H}}_2+{\mathrm{Cl}}_2\to 2\mathrm{HCl}$ has much higher quantum efficiency than  ${\mathrm{H}}_2+{\mathrm{Br}}_2\to 2\mathrm{HBr}$. 

The first step of secondary process of ${\mathrm{H}}_2+{\mathrm{Cl}}_2\to 2\mathrm{HCl}$ is exothermic while the same for ${\mathrm{H}}_2+{\mathrm{Br}}_2\to 2\mathrm{HBr}$ is endothermic.