Both have advantages and disadvantages. Hopefully the pros and cons listed below will help you make that decision a little easier.
Pros: Down sleeping bags are warmer ounce per ounce. Down is lighter weight and easily compressed. However, when storing your down bag, store it open as possible. Down filled bags are great at wicking away moisture. With the proper care down bags can last for many years, even a lifetime, so the heftier price tag is often worth it for the longevity. Down bags are ideal for all aspects of camping except wet/damp areas like for example the Olympic National Forest in Washington.
Cons: It does have a few cons. It does not function well at all when wet, and takes a long time to dry. They are also more expensive and need more care.
Pros: Synthetic bags then make sense when used in wet/damp camping situations. It works well for folks new to camping, kids, and the fiscally conservative. It dries quickly and is very easy to care for. After your trip you can toss your synthetic bag right into the washing machine.
Cons: Synthetics are heavier than down and they are also not as comfortable. They do not pack down as small as down bags can. Synthetics bags are also not as warm as natural down.
I would love to hear your thoughts! Which fill do you prefer?