Briquettes burn long, charcoal (lump wood) burns hot. So if you are roasting a whole chicken, or want to grill over an extended periode of time, use briquettes. When you want to sear in the flavor fast and have relative small items on your BBQ, you can use charcoal.
We do not recommend using wood on your BBQ. Wood can heat up to extreme temperatures which may cause your BBQ to damage.