I think that is highly dependent on the game, the conditions, and the skill/strategy of the players. For example, would you say that the player that gets to shoot first after the break in 9-ball is the favorite to win the game? At a pro level, that's certainly true. So is the break an advantage? Only if they make a ball on the break more often than not. What if the table is tight and the balls aren't racking well, so either player only makes a ball on the break 40% of the time? Would you be better off with your opponent breaking in that case?
Yeah in the leagues and tournaments that I play in, the break is probably a disadvantage. I see so many people make a ball on the break, start shooting balls in, and then fail to get out, leaving a much easier run out for the opponent. Even among pros the break and run percentage is only a little above 50%. Go down even to very good amateurs where the BnR rate is, say, 20%, and I bet the player who isn't breaking wins more often.