Thank you for the great replies!
I picked these photos to point out the different depth / three-dimensional feel that I noticed in many FF shots.
I know that the valley or giraffe are not exceptionally good shots and neither are mine.
In the first three FF shots the subject really sticks out of the frame.
I would expect the same from my last picture of the boy.
It is a little better with the girl but nowhere near the first two photos.
I really feel drawn into the valley which makes a powerful impression on me.
In my first two pictures I don't really have that three-dimensional feel dispite objects in different distances.
You don't seem to think it is the sensor.
So, how can I create that spatial impression?
The larger sensor (or more precisely, longer focal length with the same fov) helps you gain shallower depth of field, but you can do that by using faster lenses or changing the aperture setting on your existing lenses.
The background on the FF shots isn't more blurred than in my pics.
So, I don't think it is about the aperture. I've got a 50mm f/1.8 to play around with.
Do I need to catch the right light and shoot from a slight up-/downward angle?
Or could I get the effect by sharpening and brightening up the subject in post processing?
The valley shot is all about composition. You have 4 lines converging to the point in the distance, and the clouds lead the eye there. The distant mountain with the intervening haze adds depth.
In the people shots, the composition of the full frame shots is just a bit better which helps give them more pop. There are no distractions on the foreground, and the background is well behind the subject. With (2) you could improve the picture just by cropping it (the girl should be towards the left, not in the center) -- then the tree frames the shot and draws the eye in to the subject. Shoot vertical often for people shots. Avoid putting subjects in the center of the frame. Read a book on composition such as "the photographers eye" by Michael Freeman.
Changing the angle can help but not just in terms of an up/downward angle but picking a shot that aligns compositional elements in the right way, so that background content enhances the shot instead of serving as a distraction.