Really its all about the loft. So if you have a specific bag you're wondering about, next time you launder it look at it when its wet and see how much loft remains. I know my winter bag loses about 40% of its loft when wet, which isn't bad, especially because it dries quickly even if it relatively humid. There are many different types of synthetic insulation, different types of face fabrics that can affect the loft. There are too many variables to give a flat number. I've heard people say that synthetic base layers are 40% effective when totally wet, but I don't know how that carries over.
Really the best thing to do is take your dry sleeping bag, and fluff it out until its fully lofted. Take a ruler and measure 3 points on the sleeping bag to see how much loft you have and average them. Launder the bag, and measure the same 3 points while the bag is wet and average them. Take the averages and you can calculate the percentage difference.
i = initial measurement average
w = wet measurement average
This will give a pretty good idea of how much insulation your bag losses when its wet.
Synthetic will most certainly be more insulating when its wet than a down bag. Down is literally useless when wet. A wet synthetic bag, I'd still sleep in if I had to, a wet down bag I wouldn't even bother(luckily never had this happen). If weight isn't a huge concern, you could try adding a wool blanket. Wool is better than synthetic at keeping its insulation when wet. Wet wool barely looses any insulating properties even when completely saturated. It dries slower than synthetic, but synthetic is generally said to dry faster. But if you're in a rain storm and can't keep dry then wool sounds like it would have been a good option.