What is a beautiful image? Is there a formula for creating great composition?
Certainly balance is important. Aesthetic balance comes from a variety of sources. Color, light, and depth of field all should be in balance. You wouldn't want an image with only one color, just as you wouldn't want an image that is 100% brightly lit.
If balance is so important, then why is a rectangle more visually pleasing than a square, and why does the "Rule of Thirds" exist?
Well, it would seem that the human brain generally enjoys images which are slightly favoring one end of the spectrum (Unless you are Wes Anderson). So while your image should contain both bright areas and dark areas, choosing to make your subject perhaps 15% brighter than the background will visually separate him/her from the background. This is the same reason you want the background slightly out of focus, and your subject sharp. It helps tell the viewer what to pay attention to, and creates a more beautiful image. Too much balance can make things look unnatural.
This is all fine for on-location cinematography, but how does this apply to editing?
To add visual interest to your frame in post production, consider the use of split screen techniques- think beyond the composition you've created on location. While utilizing this technique, remember to keep the compositions of your frame interesting. A direct 50/50 split of your screen might not be the most visually appealing, whereas if you scale one video source to 65% of its original size, and a second video source to 35%, put one in the top 1/3, and the other in the bottom 1/3, you will have a slightly "imperfect" balance.
If depth of field is important to on-location shooting, then it should be in post production as well. Adding a blur effect to one image can draw the viewer's attention, and using keyframes so that a "rack focus" effect is created, with one image coming into focus while another goes out of focus, creates a much more kinetic energy to your composition.
In Final Cut Pro, this can mostly be done with the "Motion" tab in your viewer window. That will allow you to crop, scale, and add movement to your images, and the included "Blur" effects will enable you to create the rack focus effect.
Lastly, there are no absolute rules in regards to this: only subjective opinions. Play around with the controls, experiment, and find what appeals to you. Study classical paintings for inspiration. Just never be afraid to try something new- the undo function exists for a reason.