I want the grey cube to match the blue 2D-overlay, but as you can see, the right face of 3D-cube cannot match the right face of the 2D picture, because perspective is "stronger" on the blue drawn cube. Is there a term to describe the "strength" of perspective and more importantly, can I increase this "strength" so the grey cube could match the blue overlay better?
As mentioned in a comment, the focal length is an important property. However, it may not be the only property you need to adjust, as the dimensions of the camera's sensor are equally important. And to get an exact match you may need to consider not only the size of the sensor, but also its physical aspect ratio (your reference image may well have been taken using a camera with a square sensor and then cropped to a 4/3 aspect ratio).
You may also need to move the camera object to get a better match, e.g. zooming in while moving away from the cube, or zooming out while moving closer to the cube. And last, but not least, you need to view your cube from the same angle as the cube in your reference image.
If your reference image is hand painted, it may not have correct perspective. The error may be subtle, but it may still make it very difficult to get an exact match.
