They're both document formats, but they come at it from opposite directions. PDFs contain low-level drawing instructions for displaying their content, but usually know far less about the content itself. ePub is the other extreme- it contains structured content, but allows more leeway in the presentation of that content.

Both formats have evolved over the years to build on their strengths and shore up their weaknesses- for example, you can now embed structured content in a PDF to make it more ePub-like (and potentially reflow text in a viewer), but in practice few PDFs take advantage of this. I don't know nearly as much about ePub, but I would imagine that over the years it has evolved to allow for more control over the visual presentation of the content.

Ultimately PDF is a more universal format but ePub is a better fit for most digital books. Both formats will probably coexist for a long time.