I teach a photography class called 'Using your DSLR' but it's really mostly about teaching the students how to shoot in manual mode.
Here is the main reasoning that I give the students as to why I think manual mode is better...
Firstly, after teaching them how to use manual mode and 'getting to zero', I teach them why getting to zero is not usually the correct exposure (reflected light meter etc.) I then teach them how to determine how to get a more accurate exposure via metering and often adjusting away from zero (or using a grey card etc.).
The key point that I try to impress upon them, is that we are using our metering techniques to work backward, to figure out the correct settings for the (incident) light that is hitting the scene, not the light that is reflecting off of it. So once they have the correct settings for a scene, being in manual mode locks that exposure into the camera and ensures that you will get a proper exposure (as long as your lighting doesn't change). So essentially, once they have determined the exposure value that they want to use, they can forget about exposure and concentrate on other things like focus, composition, interacting with their subject etc.
The next day of class (usually a week later), I teach them how to use aperture and shutter speed priority modes. Those modes, on their own, basically do the job of getting you to zero, which they now know is not all that useful, so then I teach them how to use exposure compensation.
But then I point out the main difference in how we would shoot in manual, vs how we would shoot in an priority (automatic) mode.
In manual, you might find a surface or object to meter off of, I use the example of snow, which is typically 1 2/3 or 2 stops brighter than middle grey. So you would meter on the snow, dial the exposure to 2 stops above zero. By doing that they have figured out proper exposure for the light that they are shooting with. So now they can shooting anything that might be in that light, a black dog, a person in a white coat, a purple-people-eater etc. They don't have to worry about exposure, because it was locked in correct for the light.
Now to compare that to how you would shoot in automatic. You meter on the snow and dial in +2 EC...but when you then point the camera at your black dog and press the shutter release button, the camera will re-meter, this time including the black dog...and thus your +2 EC will likely give you incorrect settings. The way to do this, of course, is to use AEL (auto exposure lock). You meter on the snow, lock the exposure, then shoot the black dog.
In in manual, you meter once, then don't need to think about exposure (unless the light changes).
In auto, you need to meter and lock the exposure before you take the shot...and every time you release the AEL button, you'll need to re-meter and re-lock, which means you're constantly thinking about exposure. So in that sense, the automatic modes are more work than manual mode.
But, I do also tell them that when you have a couple of criteria met, then it's a good idea to use an automatic mode. Those criteria are 'time constraint' and 'uneven lighting conditions'. So if you are shooting in a scenario where your lighting will be different from shot to shot, and at the same time, you don't have the couple seconds it takes to adjust the settings in manual.....then it's a good idea to use the automatic modes. Of course, you still need to use EC, but that is likely quicker than adjusting 6 stops of exposure in manual mode.
At the end of the day, it doesn't really matter what mode you shoot in. A shot taken at ISO 400, 1/125 and F8 will be exactly the same in any exposure mode.