If the camera is set to save files in a lossy compression format, that will dictate te size of the file. I will bet your camera is set to save in a jpeg format (with .jpg file extension). You may also have the quality setting (always use the highest quality, btw).
All things being equal - same quality of jpeg compression on both cameras, and the same exact scene, the camera with 14 megapixel sensor will produce larger files. However, two things may be happening:
1. Your jpeg quality setting is different on the two cameras
2. Scene is different
Let me explain the second. The way compression works is it analyzes the scene and removes repeated patterns. It then reconstructs those patterns during decompression (this is a gross oversimplification, for a more sophisticated explanation see here
). If there is a lot of intricate detail in the picture, it cannot be compressed as well as a picture with large areas of blue sky and large areas of dark blue sea. Therefore, the subject matter will also dictate the size of the file. In fact, it can have quite a dramatic impact.