They both show signs of narcissism. To be honest, if you strive for power like they both have, most will have those tendencies. They both have a “Burn it down!” attitude if they don’t get what they want, and both will use half truths to further their agenda if needed. Both give a lot of time to their narrative, and not as much to their actions.
The biggest difference is that Trump is/was a business man. That means you have to face the fact that you can’t get what you want all the time, and you MUST find a way to deal with that.
So in the end, Trump is much more of a functional narcissist that Obama will ever be. Trump has had many times in his life that he had to admit “I can’t win”, and dealt with that. Obama has had very few, and has never dealt with it constructively.
Good points. A book—a very big book—could be written about the differences psychologically between Obama and Trump. Not having time to write a book, I’ll just note that Obama is a Malignant Narcissist. That is one of the worst and most destructive Personality Disorders known to man. If you’ve never read about it, you might want to take a look sometime. It is scary stuff.