Fuel consumption is a very important issue, and much besides the airplane or engine manufacturer influences the final result. Both Airbus and Boeing publish only marketing numbers, and require a non-disclosure agreement bevor they reveal any meaningful figures.
Approximately three quarters of the progress in fuel consumption in the last fifty years has been achieved with better engines, and the airframe and better operational procedures contributed only the remaining quarter. If there is any difference between contemporary Airbus and Boeing planes, it is very small, and any advantage is usually reversed with the next upgrade or new model from either company.
Here is a related question: Atlantic fuel burn estimations. It has links to tools for fuel burn calculations.
For a first approximation, use 55 to 65 g of fuel per Newton-hour or 15 to 18 g per kN of thrust per second with modern jet engines. Please do not use the static thrust at sea level, but the actual thrust at the right flight Mach number and altitude. If you lack this figure: A modern airliner needs thrust equivalent to between 1/18th (5.6%) and 1/12th (8.3%) of its weight. In cruise flight at Mach 0.82 the higher number of 8.3% should be used.
Things which have an influence on fuel consumption:
- Flight speed. Usually flying a little slower helps, but normal operations are already quite close to the optimum. See here for a related question.
- Flight altitude. Flying as high as thrust allows helps, but is not always possible. See here for a related question.
- Operating mass. Lighter aircraft can fly higher and have less drag. Excessive reserve fuel rules cause fuel burn to go up.
- Flight path. Usually the direct route is best, but sometimes gains can be made by avoiding a headwind en route.
- Proper piloting. Flying with a small amount of sideslip already destroys any advantage winglets might have, and drag goes up quickly with sideslip. This is mostly an issue for propeller airplanes, though.
- Maintenance status of the engines. Engines lose a few percent of efficiency over their operating life.
- Maintenance status of the airframe. Dirty wings or badly fitting doors produce more drag, and condensed water in the belly adds some additional weight which increases fuel burn. Condensed moisture can accumulate in the fuselage, and airliners in Africa can well have a few tons of condensed water onboard.
This is why in real life the fuel burn varies, so any published figures out of context are hard to verify.