Of the two—Wordsworth and Coleridge—who had greater influence on modern criticism?
I edited down the original question. I think that both thinkers would see their role as being equally influential. Wordsworth and Coleridge collaborated so openly on so much in terms of defining the essential points of Romanticism that their contribution would have to be seen as shared. Yet, I tend to think that Wordsworth would be seen as having a greater impact on modern criticism because of the volume of work he produced and his willingness to be so openly identified with the Romantic movement. With Coleridge, there was a desire to move into a philosophical line of thought that was more wide open about the nature of intellectual ideas. This was not where Wordsworth focused his attention. The ideas about the artist, their presence in the world, and their relationship to their art are conceptions that Wordsworth articulated and embodied in his time as being considered the leader of the Romantic movement. Over time, Coleridge was viewed as more of an auxiliary figure in this configuration, perhaps because of his own intellectual ruminations which proved difficult to classify as opposed to Wordsworth's, which were more in line with Romantic artistic inquiry. Wordsworth's ideas were influential to the "next generation" of Romantics like Keats and Shelley and resurgence of his own legacy by critics like Matthew Arnold have gone very far in seeing that Wordsworth's influence on modern criticism is profound. It is also through this where one sees that his influence has been ranked higher than that of Coleridge.
This is a tough question because it is often difficult to untangle Wordsworth's thought from Coleridge's; the two developed their ideas through conversation with each other. In fact, Coleridge would write that the enormously influential Preface to Lyrical Ballads, written by Wordsworth, was "half a child of my brain."
Nevertheless, Wordsworth arguably has had a greater influence on modern criticism because he was the one who wrote the Preface. Coleridge, suffering from opium addiction and, perhaps, too many good ideas, wasn't able to lay out the new precepts of poetry as Wordsworth was.
The ideas that Wordsworth expressed in the Preface continue to influence criticism today, most famously the concept that poetry should be "the spontaneous overflow of powerful feelings recollected in tranquility." Wordsworth articulated a theory of poetry that emphasized feeling over intellect. He also highlighted the importance of the subjective insight of the poet as all important. Wordsworth, as he expresses in The Prelude, believed the poet could actually change how people perceived reality through his poetic vision by rendering the common person as sublime and praiseworthy. This critical concept of poetry has continued to be influential.