In my opinion the Flash should be faster as Superman flies most of the time, it’s rare to see him actually run to catch an enemy, and I don’t think Superman has run faster than the speed of light.
Anyway, the question was finally answered in The Flash Rebirth #3.
In this story Barry Allen was trying to outrun becoming the Black Flash, so when Superman tries to talk to him this happens:
This next panel comes immediately afterward;
Superman doesn’t catch up to him. This pretty much clears up any doubts about who’s the faster runner, and last time I checked Superman never reached the speed of light while running, so the Flash is faster than Superman, he’s truly the fastest man alive.
You can also find a list of the many times they have raced at Hyperborea.org.