I found this hard to believe, but confirmation bias is a hell of a drug, so I ran my own quick blinded experiment: 3 cups of hot water, one of which had a small pinch of saffron swirled around in it, one with a 1/4 tsp of turmeric, one plain.

That it was trivial to tell which was which is an understatement. There's a floral sweetness to saffron that is absolutely unmistakable to me.