Let's see if I adequately can explain this in non-engineer terms
To a first approximation, props are constant power devices, while (pure) jets are constant thrust devices. The relationship is thrust x speed equals power - so the faster you go, the
more power a jet produces while the
less thrust a prop produces. So, props have better low speed performance (e.g. takeoff), jets have better high speed performance.
Modern technology has blurred that difference. High bypass turbofans pretty much split the difference between props and jets - producing adequate low speed performance and good high speed performance, while the latest high speed props provide improved high speed performance while retaining their excellent lower speed performance. But that basic relationship is the same - props are better slow, jets are better fast.
Now, that 's all engineering theory. For the specific instance of the A400M, some committee apparently made the decision that the low speed advantages of props were more important than high speed advantages of fan jets. I suspect politics played a role...