Ok i dont play with leaders so i cant really advise you on them...but why you would want to play second is to work out a better strategy
and then theres the poison abiltity Poison X, Min Y
If your character wins the round, at the end of each of the following turn your opponent will lose X life point(s) if he has more than Y life point(s). If your opponent has Y or less life point(s), the poison effect is not triggered.
Very strong in the case of Nina (U).
Ashigaru isn't that great, but going second allows you to see the first card that your opponent plays first, which can allow you to know if you play a deffensive card first or not, the poison question suicidal answered it perfectly