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 $\mathsf{Sym(4)}$.)
Here is yet another approach:
> P,phi:=pQuotient(GA,3,1);
> AQInvariants(Kernel(phi));
[ 2, 2, 0, 0, 0, 0 ]
> P,phi:=pQuotient(GB,3,1);
> AQInvariants(Kernel(phi));
[ 0, 0, 0, 0 ]
In fact these three methods are all detecting the same difference in finite quotients of the groups, but I included them all to give you an indication of possible techniques for proving non-isomorphism.
Ultimately, all of these techniques rely on looking at various types of computable quotients of the groups. Unfortunately there are examples of pairs of non-isomorphic finitely presented groups which cannot be distinguished in this fashion by their computable quotients (in fact the unsolvability of the general isomorphism problem implies that such examples must exist.)