but who is to say which one is truly "better"?
anyone. this guy fails to understand the difference between "objective" and "subjective", just like pretty much everyone else. in fact, there is no difference. the distinction is only helpful as shorthand.
when people say something is "objective" they really mean "no one is able to disagree about this". hence, the only things considered objective are those that are so simple and vary so little from one person's perspective to another that they appear identical, things like spatial measurements, logic statements (which are purely artificial anyway), and all kinds of numerical data. over time, more and more things have fallen into the realm of "objectivity" as we make conceptual advancements (in other words, new measures) and technologies to support them (e.g. scales, microscopes, computers, etc.).
but the fact of the matter is that there is no verifiable, transcendent "truth" to any of these so-called "objective" measurements... they are all verified subjectively in the end. just because everyone agrees something is the case, doesn't mean it is the case... but it does mean it's "objective". furthermore, there is no verification of any sensory stimulus by "the intellect". we can never know the nature of our sensations in non-human "objective" terms. to do so would require us to be "outside" our own consciousness, something which just isn't possible.
however, some day in the future, we may even have ways of measuring and understanding much more complex functions of human consciousness such that we can "objectively" rank beauty judgments. in the meantime, anyone is free to say whatever they believe is right, and those who can convince the most people to agree with them will win, and therefore "define beauty". this brute force method actually happens in science as well, even though most people wouldn't admit it, and the level of consensus required in such a rigorous atmosphere is basically 100%.