It's up to you, really. Both pieces of software can handle position and scale keyframing, and the results will be virtually the same.
If you wanted to get fancy and have motion blur on the videos when they grow and overtake the screen, you'd want to use After Effects.
If you want to save a tiny bit of time, Premiere Pro should be able to accomplish this no problem, without needing to even open After Effects.
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Do you have experience in After Effects? This would be a good project to dive in and learn keyframing, easing, geometric adjustments, simulated drop shadows (possibly using expressions to link them to the scale of you moving objects) and the differences between doing this in 2D or in 3D with a virtual camera and some lights that would create real shadows.
As soon as you go to 3D in AE, though, your rendering time explodes, increasing geometrically with each light, object, effect and enhancement.
Both thanks for your advise!