My general advice to younger people on the topic of "looking for work" is "are you ready to go where the work is?" That is not specific to engineering of any flavor.
On aerospace engineering specifically: I actually have a B.S. in Mechanical, but I wish I had double-majored in Aero because the required courses overlapped so much (I went to Cal. State Long Beach). IF you can stomach it, I would recommend that route.
I chose Mechanical actually on the advice of an engineer who himself majored in Aero. His reasoning was (and I generally agree): Mechanical Engineering has more applications than just the Aerospace industry - you can work in automotive, civil, construction ... literally anything that has structural or mechanical workings will have a need for someone with that background. If you major in Aeronautics however, your fields are somewhat more narrowed and specialized...however^2: As Psyborg rightly points out there are quite a lot of aerospace applications popping up, between numerous eVTOL, commuter/UAV and other aerial vehicle startups. In addition to that I wouldn't be shocked if the SPACE end of aeroSPACE picks up in the coming decades. And you CAN still use an aero degree in the automotive industry; they do wind tunnel testing of high-end models, and racing teams use it even more-so, but those are (like I said) a bit more specialized and likely not "entry level" positions.
I definitely do NOT think an Aero or Mechanical Engineering degree would be wasted on anyone, even if you don't end up going to be a famous aero or auto designer. Here's why:
In order to get one of those shiny engineering degrees, you have to take a LOT of classes that teach you nasty things like statics, dynamics, physics, calculus, and electromagnetic theory. Guess what? Along the way, by passing those classes, you will acquire (by necessity) incredibly valuable and increasingly rare skills of critical and lateral thinking, multi-variable analysis, deductive and probablistic reasoning, and logical and rational discernment. For THOSE SKILLS ALONE I would recommend a double-major in Aero-Mechanical Engineering. I'll even throw in Electrical Engineering - there's a massive shortage of electricians (and general contractors) in my area, my wife is about ready to go back to school herself if we can't get electrical work done!
And then if you DO fancy actually using your degree, you can take it to Boeing, Lockheed, Northrop, Rockwell, SpaceX, Blue Origin, Swift, Wing....ALL of which I know are hiring in some engineering capacity, and those are just off the top of my head. Go browsing on LinkedIn and you'll get swamped!
Hope that helped! Good luck!!