I've been talking to people outside of physics and a topic that has come up fairly regularly is what general skills does physics teach you. I've spoken with a couple people with bachelor's degrees in physics who are now working in software and they said that physics teaches you systems level thinking. I guess that's a good answer if you're applying to a software job. But I feel like "systems thinking" isn't the most satisfactory answer. If that was all you learned from physics, I don't see why you couldn't study another subject. There must be other academic fields that teach big picture thinking.
So I'm going to try and give my own answer. "What does physics teach you?" Physics prizes knowledge that is universal, enduring, and predictive; information that is too idiosyncratic and transitory is considered "uninteresting."  When you study physics, you assimilate these values. You can scan information and pick out the things that are universal and enduring and things that are idiosyncratic and transitory. The former you pay a lot of attention to, and the latter you assign low priority. When you're unsure how to categorize piece of information, you instinctively look for sanity checks.
In general, all serious academic fields value universal, enduring knowledge. However, there is one difference. Physics can predict the future. Physics possesses a bounty of beautiful and (most importantly) wildly accurate mathematical models -- where if you have enough information about the initial state of the system, you can make specific, quantitative predictions about how the system evolves. No other natural or social science has had this kind of success. And having all these successful, sophisticated models leads to a deep understanding of nature. When you study physics to a sufficiently high level, you experience the nirvana of deep understanding.  It's hard to become a deep thinker if you don't know what deep understanding looks like. So this is the gift of physics. It's the quantitative field of study that makes deep understanding most accessible. 
Studying physics molds you into an efficient, discerning, deep thinker. 
 Physicists (in my experience) also tend to be pragmatic, rigorous, and suspicious of hype. They're after the truth and reluctant to say things they're unsure of.
 If you're like me, that feeling is intoxicating and you want more of it!
 You could probably argue that some types of math lead to the same kind of deep understanding and thinking.
 When I took freshman physics in college, I picked up these impressions and got a taste of "deep understanding" which is why I ended up majoring in physics over other subjects. I sensed something greater than myself, that transcended human experience. It was a transformative experience and I wanted more.