I have been using CSS for many years now, and I have always been a 'percentage' kind of guy, as in I always define heights and widths using percentages as opposed to pixels (except, for example, when setting things such as margins, padding, etc, in which case I use pixels).
I would do something like this:
Mobile webpages. %'s rock for that. As it will (obviously) adjust to suit.
However when you want a fixed width for say example an article of text that you want displayed in a certain way, px's is the winner.
Both have many plus's and minus's over each other :)