One (little cunning) advice I received to deal with 'battle of egos' was to introduce a third person, a third reviewer to break the tie. Ideally the person should be one to whom you both respect (due to authority or whatever) and are ready to take his/her word. Cunning part can be he/she should be the one you know will agree with your review comments/thoughts (which should be easy since you know your concerns are valid). This is assuming such battles are rare and people are open for genuine review comments.