Power
A senior audio engineer is likely to have several people working under him or her. Being in charge of an entire sound production is a big responsibility, which is why they wouldn't put the operation in the hands of some unproven young punk. They are much more likely to go with a veteran of the biz with a nice prestigious track record. The audio engineer-in-command of a big production oversees all of the other engineers working on the project. That said, even if you are the tippy-top boss-man in this field, it's not like any decisions you make are going to be affecting world trade.
Plus, you are still probably working on someone else's project, which means there will be someone who you answer to. You're not the creative genius behind the production, just the person who keeps the dreamers in check and makes sure that it doesn't all fall apart. There's a reason that "engineer" is part of your job title—you make things work.
An audio engineer working a live event has the power to pull the plug, but you could probably only do that so many times before you stop getting hired. The most important thing an engineer in charge can do is not be too controlling. Your colleagues in this field are sure to be competent and talented people, and no one likes a bossypants. You're better off to leave the power trips to Kanye.