Wouldn't the way the word was used determine its meaning (or whether it had meaning at all?) Certainly, we often use the term "beautiful" to refer to our subjective enjoyment of an object or situation. But is it possible that there are circumstances where the term's use implies more than subjective content? If so, comparisons are not nonsensical. The question seems to be: what are the circumstances in which such a comparison could meaningfully take place?
In the development of modern Western aesthetics, where debates about relative beauty are relevant, a certain homogeneity of artistic purpose or common aesthetic criteria were accessible to support or dispute a value judgment. Assumed, i might add, both by the people appreciating the works and the artists creating them. For example, when Kant was working on the Critique of Judgment
European painting was almost exclusively realist. The value of the painting was determined by the accuracy of the painting's portrayal of it's subject and the effectiveness of the style. (The degree to which the Enlightenment sense of beauty relied upon the distinction of style and subject should probably be taken into account. As style has assumed greater importance than subject matter, or more appropriately as the two concepts are increasingly seen to be indistinguishable, the appeal to common aesthetic principles has become more difficult as styles proliferate.)
It might be difficult to determine, personal preference aside, which would be more beautiful when comparing two very different objects. But if the two things share enough features, or are subject to the same criteria, then a judgment of relative value might be meaningfully made as regards even so ephemeral a quality as beauty. Two paintings might be compared based on the skill of the rendering and similar stylistic technique, even if the two paintings represent different types of subject.
On the other hand, if two people are engaged in debate regarding, say, the beauty of a painting of a sunset vs. an actual sunset, i think things become more complicated. I don't think that this comparison is meaningless, but the principles upon which one would base a judgment are certainly less clear. It could not be based on the accuracy of the representation, obviously. Perhaps it would require the interlocuters to agree upon the beauty of a third object in order to gauge their respective appreciation of the objects in question. In the example above, what if the two people agreed that the sunset two evenings before was the most beautiful both had ever seen? Then they would have something to compare both the painting and the current sunset to. As they enumerated the similarities and dissimilarities of each of the debated objects to the perfect sunset, they could slowly peel away their respective personal reasons for preferring each thing, the painting and the view, and come to an agreement. (of course, in a way I am kind of falling back on the principles I relied upon in the first example, since the actual sunset being evaluated is sort of being critiqued as it resembles or represents it's "perfect" counterpart. Perhaps that invalidates my point.)
These sorts of considerations sometimes open our eyes to aspects of things that our immediate, personal take does not. One's understanding of beauty can be both broadened and deepened. Of course, just as often this is not going to happen, and the word beautiful will remain both contested and a mere stand-in for the word "preferred."
Edit: I reread this post a few hours after I wrote it. I found some of the phrasing a bit clunky and roundabout, so I've edited it for clarity's sake. Hopefully, I've managed to make it a little less clumsy. I've also pointed out a potential weakness in my argument that I noticed during my revision.