The proxy fights that you mention here are discussed in Chapter 5 of Outliers. The way in which they are characterized is in keeping with the point about success that Gladwell is trying to make in this part of that chapter. The proxy fights are characterized as being somewhat corrupt and dirty and generally very unsavory.
I only have this book on Kindle, so I cannot give page numbers, but you can find the discussion of proxy fights by looking up “proxy fights” in the index. Gladwell describes the proxy fights by quoting at length from “the legal historian Lincoln Caplan.” Caplan’s description makes the proxy fights sound rather unsavory. First, he calls the place in which the fights were decided “the snake pit.” This makes the fights sound dirty because it likens the lawyers involved to snakes. He talks about the adversaries wearing t-shirts and drinking whiskey during the proxy fights. He mentions that they would try to cheat by getting inspectors appointed (the judges in the fight) who were “beholden” to them. He then describes Joe Flom (the subject of this part of the chapter and a proxy fight lawyer) as “a hundred pounds overweight” and as “physically repulsive.” He says, for example, that Flom would “fart in public… without apology.” In short, by quoting Caplan, Gladwell is characterizing these proxy fights as very unpleasant things conducted by people who were equally unpleasant.
This fits in with the point Gladwell is making in this part of the chapter. The point here is that one secret to Flom’s success was accidental. Flom was Jewish and top law firms at that time (1950s and 1960s) typically did not hire Jews. So Flom had to work for himself and he had to take jobs that no other lawyers would take. The proxy fights were one example of these because they were seen as too seamy for the high class law firms to take. Sometimes, Gladwell is saying, success can come from being put in a disadvantageous position.
Thus, the proxy fights are characterized as rather unpleasant, which helps to explain why Flom got them.
I am unsure as to how much detail you were looking for, but the proxy wars were legal maneuvers at the center of any hostile take over bid and could therefor be characterized as rather hostile and competitive.