I agree that saying a bike is 'climber' is hyperbole at best. However, I have noticed significant differences in feel between bikes when climbing (as well as accelerating, descending, and even braking) on different frames with the same equipment. Some will say that frame weight, or weight overall is what makes a frame a better 'climber'. Not in my experience. There is a certain balance between stiff and flexy; which should be distinguished from 'lively' (defined here as snappy; flexible but resilient). The closer to totally stiff you get, the more 'dead' the ride becomes. The closer to flexy, the more unsure it will feel, even to the point of being unpredictable. The weird thing is that sometimes a flexier frame that feels like springs or snaps back with each pedal stroke. This can is a very desirable trait to some riders. It's a feel often attributed to bikes with frames made of Columbus SL steel. That feeling is somewhat pleasant can cause a bike to feel 'alive', which more than likely triggers an psychological response that causes the mind to think the body is feeling stronger or more fresh. Is it a placebo effect, as far as actual performance is concerned? Yes. Do frames really posses levels of springiness/stiffness and other desirable ride qualities that the body interprets as faster, stronger, lighter, stiffer? Yes.

The fact is, that the riders desired level of the aforementioned springiness quality will cause some riders to want to climb more and have fun doing it. Thus, the answer of which bike is better for climbing, is the one that you enjoy the ride/climbing qualities of the most.