What the hell is a pixel?

This depends entirely on the element you're sizing, the text it contains, and its relationship to the page.

In short, design. You use the tools available to achieve the best designed results.

For example, things measured in characters:

- the human eye finds it easier to read large blocks of text that are approximately 60 characters wide

- First-character indent makes more sense in terms of ems than pixels if your site's font size is ever going to change (which flexibility is the whole point of CSS, right?), as does inter-paragraph spacing and other design elements

Things measured in pixels:

- Device screens often have a fixed width that's measured in pixels

- Images have a defined size (although you may wish to scale this)

- In conjunction with the above points you may wish to size a paragraph to fit some other page element and the device's screen, or even size a single character at the start of a piece.

...and of course for very specific applications you may wish to size things in physical units such as cm or inches.