The very mention of some level of the ability to perceive a week-written composition infers objective information being used to make the distinction.
Yes, there are certain objective stylistic traits in a work of the 18th century - but these traits were shared by all of the composers of time of Haydn, Mozart, and Beethoven. The audience of that time was much more familiar with this style, and actually heard it differently than we can today since for them it was second nature. It wasn't until about 100 years (~ 1840) after the fact that the term "sonata-allegro form" was codified into music theory.
When Haydn was writing what today we call a sonata form movement he did not think in those terms, nor did his audience. Haydn, and all of the composers of his day wrote movements which later came to be called sonata-allegro form and generally the Classical period style was recognized. But Haydn was simply writing in the style of his period - but perceived to have been doing it better than his peers. At least that is what is evidenced by contemporaneous accounts.
Haydn, Mozart, and Beethoven were considered great during their lifetimes, for bringing the prevailing style of their time to its highest level, and that judgment has continued to this day.
But this determination is somewhat soft in that there are still many variables and judgment calls which are subjective in nature. How much better was Beethoven than Hummel? This kind of question cannot be answered, or if so, differently depending upon which scholar you ask.
But the bottomline is that their music continues to be relevant and meaningful to us, and it is not simply because we have been repeatedly taught that their music is great.