I have to agree that these are two instances in the novel that, at first glance, don't seem to have very much in common. However, one point of comparison between the two lies in the fact that who people appear to be on the surface is not always who they really are underneath. I think a lesson that Scout and Jem learn from this is that you can't make assumptions about people and expect them to be unequivocally true. This lesson serves them well later in the piece (or at least serves Scout well) with regard to understanding Boo.
Here is where I see the most direct comparison between the two incidents. Atticus hides the fact that he is an excellent shot because this is not something that he is really all that proud of (shooting is a last resort for emergencies in Atticus' viewpoint). It is not a character trait he feels his children need to emulate, but he is courageous enough to do what must be done. What Jem and Scout learn about courage from this scene is that true courage is silent. It comes out when the time is right, when it is needed. It is not something that you need to brag about, nor is it something that you should ever have want to have to use.
Ms. Dubose, too, has a hidden self - the struggling addict who is to be both admired for her strength and understood for her suffering. She does not want pity, even though her desire to hide her weakness makes her appear to be a mean old lady. Jem learns to view her differently when he sees the truth and the pain that she suffers. He learns that sometimes there is courage in just surviving.