Finance jobs are a) hotly contested, b) actually involve much higher work hours (mergers and acquisitions positions could well work 18+ hours a day, 6-7 days a week for weeks on end for major deals) and c) salary figures are very misleading as much of that is due to bonuses; poor performance by an individual or failure to "suck up" to the bosses could net much lower figures
Engineering roles on the other hand are moderately contested at very well known companies, but salaries are consistent even among smaller regional roles with major international congolmerates. Additionally it is a constantly growing sector that is constantly facing a shortage of skilled workers, unlike finance where there are only so many positions needed, and so many beyond that offered in addition. Also working hours tend to be fairly standard 9-5 (certainly within aerospace, chemical engineering roles in the oil and gas industry may involve some more shift oriented work if offshore engineering roles are considered).
To go into aerospace you would need an engineering background. Most fields are applicable in different roles; materials and civil engineers can focus on structural elements, while mechanical engineers may handle that as well as propulsion aspects. Electronic and computer engineers may work in avionics, networking and control systems engineering. Aerospace engineering graduates may end up working in any of those areas depending on specialism.
Finance requires any degree; quantitative preferred. Usually "brand name" of the university and the degree being perceived as "rigorous" is more important than any specific prior knowledge. Many engineering graduates move into finance and banking roles in addition to engineering roles, and are highly considered by employers for them.
At the end of the day, both roles offer a generous salary, which in either case is more than enough to live comfortably on. Engineering roles allow you to do this while working regular hours and allowing you free time, finance requires you to constantly be gunning amongst your colleagues to get noticed for the slim chance to, much later, move into a management role where not much is required of you and you'll get to spend the last 15 years of your life playing golf and driving a mercedes before dying of a heart attack at 63 (ok a slightly biased view, but you get the point).