Hmm, it's hard to respond to this -- I don't have samples to post because I never shoot in Green Box mode. I shoot either in Manual or Av.
But, it sounds like you need to take some time reading up on your digital photography -- there are good books and websites that cover a lot of ground both on digital photography in general and also on the specifics of using your camera (go to Amazon.com and search for your camera and you will find books by, for example, David Busch and Magic Lantern).
And, there is a wealth of info here on POTN! In fact, one of the "stickies" at the top of this page is a favorite for people new to photography:
https://photography-on-the.net/forum/showthread.php?t=414088
In general, the Green Box Mode is, simply, Full Auto, meaning that you are letting the camera make all the exposure choices for you as well as processing choices (such as setting a Picture Style). So, if you are totally inexperienced with getting a desired result from your camera, then sure, the Green Box mode can take a shot for you. That's how many people go!
But, people who want to "get serious" about photography will take the time to learn about how to do more with their cameras. Of course you can go from Green Box to other Auto modes like Portrait, Landscape, Action, etc, and, if you read your camera manual or one of the books I mentioned there are some "clues" about those modes, and they can actually "get you started" in learning how to work with your camera.
Then, it just keeps on getting more involved and interesting. Learning how to work with Picture Styles is something you can get started on as soon as you make the move out of the Auto modes -- the Picture Style determines the overall "look" of the jpeg the camera produces in terms of Contrast, Saturation and Sharpness, things which tend to mean a lot to people. And, out of the Auto modes, you are also making choices about how you want the aspects of your photo to come across -- how fast do you want your shutter speed to be, for example? In the Auto modes you switch between different modes, but the camera makes the actual choices, whether you want things that way or not.
Finally, comparing images between a Green Box image and something like a shot done in Manual will be pretty meaningless simply because it will largely depend on the individual photographer and his/her skill with the camera and with any needed post-processing. Many photogs take control of those things and produce amazing images. Many are just fiddling around and learning and their images will tend to show that and be "so-so".
I'd say, go out and shoot and learn as you go, do some of the research I suggested, then go out and shoot some more. If you go to an Auto mode and get a shot you like, study it -- look at the aperture, shutter speed and ISO that the camera used, and you can learn from that and use that knowledge for when you want to try Manual or one of the semi-auto modes like P, Av or Tv. Experiment, but make sure you do your "homework", reading your manual to understand how to do specific things and reading more of the broad resources that will help you understand digital photography in a broader way.