<p>From what I’ve seen, skills > major. Granted, a degree comes with an amount of knowledge, but if you can demonstrate knowledge with an imperfectly compatible degree, you’ll still be in the running for a job.
Physics is often simply “quantitative finance” although some schools start to offer Financial Engineering, which fill that role. Keep in mind people in finance with a little too much money on their hands may have other interests.
Even with the extremely cyclical nature of Aero (gets hurt more by busts), it simply seems to be a better fit than the others. Complement your education with EE/CS electives if you’re interested.
Ultimately, experience trumps education. Of course you could get screwed if your potential employer decides to be a hard-ass (this happens during worse recessions), but it’s not a killer if you gain good experience through university/work experience.</p>