As RedGrittyBrick showed, the aircraft are certainly similar in external dimensions, with the A400M being a bit smaller than the C-17. However, the differences are in what the aircraft are designed for. The C-17 is designed to carry heavy cargo long distances, while the A400M is designed to carry lighter cargo shorter distances.
The C-17 is powered by 4 turbofan engines which can together produce 160,000 lbf of thrust. The A400M is powered by 4 turboprop engines that can together produce 44,000 shp, which will come out to probably less than 30,000 lbf. Though both types of engines lose power with altitude, the turboprop will also lose more power with speed.
The difference in power corresponds to a difference in the weights of the two aircraft. The C-17 MTOW is 585,000 lb, while the A400M MTOW is 310,852 lb. The max payload weight is similar: 170,900 lb for the C-17, and 81,600 lb for the A400M. The C-17 is about twice as heavy and can carry twice the payload as the A400M. The C-17 also offers a larger cargo area, with 1.5 m extra width and 3.7 m extra length.
Due to the similar size, both aircraft can carry a similar amount of troops. The C-17 carries up to 134 and the A400M carries up to 116. However, the C-17 can only carry 102 paratroops, while the A400M can still accommodate 116. The A400M can also accommodate 66 stretchers, while the C-17 can only accommodate 36. This illustrates that the A400M is designed to carry lighter cargo such as personnel, but the C-17 isn't really more capable.
As RedGrittyBrick also mentioned, this leads to a difference in roles. The powerful turbofans on the C-17 can carry a lot of payload, but they need longer distances to make up for the higher fuel consumption. The C-17 can fly 2,420 nmi with max payload, and the A400M can fly 1,780 nmi. Similarly, the C-17 can fly 5,610 nmi with paratroopers, while the A400M can fly 3,450 nmi with a 20-tonne payload.
Based on Source