Page 31 explains damage barriers in detail.
To answer your question, yes...traits on either creature (defender or attacker) can modify the damage barrier roll.
On another note, damage barrier is not a counter attack. That is an entirely separate step in the attack sequence.
Damage barriers and counter attacks are different in two important ways. Damage barriers only go off if the attacker does damage to the defender, counter attacks go off regardless. Second, damage barriers go off even if the attacker does enough damage to kill the defender. Counter attacks do not.
Hope this helps.