For a bit of ancient internet history: http://style.cleverchimp.com/font_size/points/font_wars.GIF
[1] http://snook.ca/archives/html_and_css/font-size-with-rem
If you don't need to support IE8 you should start using rem today.
[1] http://stackoverflow.com/a/4531441/1971539
[2] The 'em' unit is equal to the computed value of the 'font-size' property of the element on which it is used. The exception is when 'em' occurs in the value of the 'font-size' property itself, in which case it refers to the font size of the parent element. It may be used for vertical or horizontal measurement.
"(For completeness, I should mention here that the "em" and "ex" units are exceptions to the above. The lengths 1em and 1ex do vary relative to the other units, because they depend on the font in use.)"
I'll update this to say "font size" as I didn't mean to give the impression that it was dependent the choice of font.
Use em when you don't care about the exact size, you just want some space.
Em is also a poor choice for borders.