Julain D. W. Phillips examines the question in an article at Bullion Vault, and his answer is none of them. The U.S. dollar will stay in place because it's the world's reserve currency. We know the problems the U.S. economy is facing, but world demand for greenbacks is too entrenched for those problems to impact the greenback yet. The Euro won't collapse for a similar reason: the PRC government is moving into Euros in a big way, as they have with greenbacks. This gives the government of the world's hot developing economy a large vested interest in sticking with both currencies. The volume the PRC govenment owns is so huge, they can't offload it except slowly. (Moreover, a currency collapse would accompany an economic collapse in the associated country or region. Mainland China cannot afford that.)
As for gold, its rise is built upon world inflation, including the inflation to come. Gold will not collapse until austerity programs fix those problems. There's no sign that the U.S. or European governments are getting their fiscal houses in order (except for the U.K. and Ireland.) So, there's little reason to expect gold to collapse either.
The common sense above goes a long way. Neither currency has to collapse into rubble to see gold acting as a trouble indicator; we've seen so for the last ten years.