That's an interesting question! There's no real hard and fast answer. But as a general rule, high-end synthetics such as PolarGuard 3D or PrimaLoft offer the same insulation, ounce for ounce, as down rated to around 600 to 650 fill.
For instance, a typical synthetic-fill bag rated to 20 degrees, such as The North Face's Cat's Meow ($169), weighs 2 pounds 10 ounces, virtually the same as the 600-fill down, 15-degree Blue Kazoo ($249), also from The North Face. Marmot's 15-degree Helium ($369) uses 850-fill down and comes in about 4 ounces below the other two bags, despite its lower temp rating.
You see a similar differential in cold-weather bags. Mountain Hardwear's Lamina -30 synthetic-fill bag ($245) weighs a fairly hefty 5 pounds 9 ounces. Feathered Friends' -25 Ptarmigan, on the other hand, comes in at 3 pounds 15 ounces.
Of course, the Ptarmigan also costs a bunch more—$709 in the eVent shell version. And that's one difference between synthetic and down: down almost always costs more, especially in the more exotic high-fill bags. In my experience down also packs into a smaller space. And because down-fill bags typically are softer than synthetics, down bags “drape” better and so can seem a little warmer.
The real difference, however, is that a soaked synthetic bag will still retain about 60 percent or better of its insulating ability, and will dry our relatively quickly. Down actually can soak up quite a bit before its insulating capabilities are really degraded, but once down gets wet, you're cold. And a wet down bag takes a LONG time to dry out.
So I usually recommend synthetic bags where cost is an issue, or the camping is apt to be really wet. In all other cases I favor down. In my view, it's still measurable better in most ways.