Difference in Magnification

I have a Sony Alpha A200 with a Sigma70–300mm lens, which gives me an equivalent focal length of 450mm (in 35mm parlance) at the telephoto end. On the other hand, my sister uses a Sony Cyber-shot DSC-H50 that has an equivalent focal length of 465mm. I shot the moon with both cameras at the telephoto end. Despite the fact that the compact camera zooms in closer, the photograph shot with the DSLR at the telephoto end seems to be closely cropped. How is this possible?
Sandeep V Khambait, via email

The difference you are seeing is not due to different focal lengths, but different resolutions. The Sony Cyber-shot DSC-H50 is a 9MP camera. The maximum size of images shot by the camera is 3456 X 2592 pixels. On the other hand, the Sony Alpha A200 is a 10MP camera that gives a maximum image size of 3872 x 2592 pixels. Thus, when you zoom in to both images at 100%, the photograph shot by the 10MP A200 seems to be closely cropped.

This is also the main reason why people prefer cameras of higher resolution. The extra pixels give you more freedom to crop, and still get a decently sized image.