What does "Water, is taught by thirst" have in common with "Success is counted sweetest?"
You have picked two excellent poems to compare and contrast! Unfortunately your original question asked more than one question, so I have had to edit it to just focus on the similarities between these two poems.
Both of these poems are carefully built around paradox. "Water, is taught by thirst" contains many paradoxes as Dickinson seems to be pointing towards the paradoxical nature of so many aspects of life:
Water, is taught by thirst.
Land -- by the Oceans passed.
Transport -- by throe --
Peace -- by its battles told --
Love, by Memorial Mold --
Birds, by the Snow.
Note how this list shows how concrete nouns are defined often by their negatives - peace is defined by "its battled told", for example. In the same way, in "Success is counted sweetest" the whole poem is built around the fact that it is only those who "ne'er succeed" who can fully understand success and count it "sweet." She offers us a scenario of a victorious army, none of whom, we are assured, can understand the "definition / So clear of victory" as the dying soldier who in his last moments hears the triumphant noises of the opposing forces.
One of the remarkable aspects of Dickinson's poetry is that she forces us to see concepts and ideas in completely different ways and often uses paradoxes to present them and really make us think about the nature of such things as "success."