The following calculations seem to distinguish between them.

    >  #LowIndexSubgroups(GA,4);
    30
    >  #LowIndexSubgroups(GB,4);
    26
They have different numbers of homomorphisms onto $A_4$:

    > #Homomorphisms(GA,Alt(4),Sym(4));
    5
    > #Homomorphisms(GB,Alt(4),Sym(4));
    1
(The options third argument $\mathsf{Sym(4)}$ means count (surjective homomorphisms) up to conjugacy in $\mathsf{Sym(4)}$.)