A paragraph break (hit Enter or Return on the keyboard) is always more meaningful than a line break (hit Shift + Enter or Return on the keyboard). A paragraph break inserts what looks like a double-space in between one line of text and another, and allows screen reader users to parse the information on the page more readily.
Although programs like Microsoft Word have options to create single-spaced documents with paragraph breaks, web pages do not. You may find using a line break more esthetically pleasing than a paragraph break, but line breaks can create problems for screen reader users.
While a screen reader can interpret a paragraph break as "blank," a line break may not be indicated to the user. The text on the new line may sound like a new sentence, instead of the start of a new paragraph.
While the line breaks may "look better" for a visual reader, a screen reader user will hear the poem that is split up with line breaks as one contiguous sentence: "Mary had a little lamb, his fleece was white as snow, etc."