What is the difference between bond angles in cationic species of ${\mathrm{PCl}}_5$ and ${\mathrm{PBr}}_5$ in solid state? 

${\mathrm{PCl}}_5$ and ${\mathrm{PBr}}_5$ are symmetrical and have same B.A. which is equal to $109°28\text{'}$degrees.

Thus, the difference is zero.