"Success is Counted Sweetest" deals with interpreting analogies. She compares a thirsty person's appreciation of a drink to a loser's appreciation of victory. It expresses how those who have failed at anything are "thirsty" for success. Those who have never succeeded want it worse than those who are accustomed to succeeding and have lost the desire or the desperate taste of it. The person left dying on the field can define more clearly what "victory" means than the person holding the flag which signifies his side won. The want of it burns more clearly in the bosom of those who haven't enjoyed it than in the hearts of those to whom "it" has become too familiar.
"Much Madness Is Divinist Sense" is a paradox. There seems at first glance to be no truth in it, but on deeper examination, we find the truth is there. Emily suggests that "madness," too, is a gift from the Divine. How often have we heard that there is a fine line between genius and insanity? She goes on to say that those who go against the majority are often thought of as being crazy and are shunned. To the speaker, such madness is actually divine inspiration. Sometimes the ones who seem the craziest are making the most sense--if you are able to have a "discerning Eye" to detect it. She also warns that society is quick to judge those who do not conform to expectations and they will be treated as dogs...with chains.
These poems deal with the meaning of things. In the first, Dickinson is saying that the person whom society considers insane might be the sanest person of all. Individuality is more important than conformity.
In the second poem, the contradiction is that we appreciate most the thing we don't have. Success is not as valuable to the successful person as it is to the person who longs to succeed. The loser of a battle knows the definition of "victory" better than the winner does; for the loser, victory cost more.