"You cannot do wrong and feel right. It is impossible."
      -Ezra T. Benson

This quote is trying to advice you to do good, to do right. You can't feel good and do bad, or do good and feel bad. If you do good you will feel good, but if you do bad you will feel bad.
-For Example:
   1. If you steal something, you cannot feel good about it.
   2. If you study hard, you will feel good by getting good grades.

   

"When I do good, I feel good. When I do bad, I feel bad."
      -Abraham Lincoln

This quote is trying to say that whatever you do, you will feel either good or bad depending in what you did. 
*For Example: 
-If you give food to a Homeless, you will feel great because that is such a Nice thing. 
-In other hand, if you kill someone, you will feel bad. Maybe not that moment but, you will because that is a bad thing.