One of the problems with defining 'classical' poetry is that the term is used to mean two very different things. All the poetry of the Greeks and Romans is called Classical, but there are not really any common characteristics to such a varied canon of work.
The other use of the term 'Classical' is to distinguish the main movement in European writing between the end of Renaissance Humanism and the beginning of the Romantic Movement. These writers are also called Augustans, and in French they run from about Ronsard to about Chateaubriand, in English from probably Dryden to Coleridge.
In this sense, Classical writers tend to focus on social issues, where Romantic writers tend to foreground the individual. Pope writes about the literary scene in London (the Dunciad), whereas Wordsworth writes about going for a lonely walk and finding some daffodils. Classical writers tend to overvalue clear and precise thinking (Pope's Essay on Criticism), Romantic writers are more interested in dreamstates (Coleridge' Ancient Mariner). At a formal level, Classical writers favour strict metres (almpst all Dryden's important work is in heroic couplets) where Romantic writers prefer free rhythms (Wordsworth's Ode on the Intimations of Mortality).
It is difficult to say exactly what the difference between a Classical and a Romantic writer is, but once you have a feel for the distinction it is easy to make.
Much as it is difficult to say what the difference is between a crooner and a rockstar - but Bing Crosby doesn't sound anything like Michael Jackson.