Is synthetic or real down warmer?
There is no doubt that real down is a better insulator. Any real down jacket will be significantly warmer than a comparable synthetic down jacket. With that said, that doesn't mean that real down is always the way to go. There are other things to take into consideration.
The first thing to think about is what you are using it for. Synthetic down has gained in popularity in recent years because of its versatility. It can be worn as an around town jacket, is great for layering, is great for active pursuits and performs better in the elements. Real down may be warmer but you don't want to sweat in it and you don't want to get caught in rain or snow in it. You can layer a real down jacket but because they are generally puffier making it a little more difficult. Synthetic down usually have a slimmer profile allowing them to fit over a fleece or under a shell more easily.