I would rule that whichever one was most advantageously to you would apply.

Say you're a scout//rogue. You get skirmish, and sneak attack. Now, you can choose to move 10 feet and apply skirmish extra damage, or you could somehow catch them flatfooted or flanked and get sneak attack damage without moving. But if you move 10 feet and catch them flatfooted, you don't get double damage.

Of course, that is reading a little bit between the lines into the spirit of the rules.