Killua and Illumi’s relationship is extremely important for both their character arcs. Moreover Killua has been deeply influenced by his older brother and both siblings have been influenced by their family situation.
Let’s note for example that both their powers make use of the high tolerance to pain they developed thanks to the training they were subjected since they were children:
So when considering these two characters one can’t avoid addressing also their famililiar environment and how it has molded them.