Don't decide the major. Look at the requirement of both majors, there are a lot of common classes, Calculus, ODE, PDE, computer language like C++, CAD, Physics, Chemistry, basic circuits...You can enroll in those and it'll keep you busy easily for a year. Then take the time to feel them out.
Another important thing is to enroll in the labs. Get your hands dirty and see which way you prefer. I learned my lesson. I was a Chemistry major, I love the theory and I got straight A in all the lecture classes in the whole 4 years. But I hate doing the lab and I got low grades. But that's where the problem lies, I don't like the lab, that's not going to fly at all. I ended up never worked a day in chemistry. I like to tinker with electronics, I modify my guitar amp to do things beyond the time in the 70s, I found my passion and I made a full career out of electronics.
Important thing is follow your heart, not your brain. Don't let good time or bad time determine which way to go. Life is too short to take the second best. I am a true believe to follow your passion. Your mission is to find out which one is your true passion. BUT, if you cannot decide, then take both. There are opportunities that can use both. I wish I know more about mechanical design also. I had an opportunity of becoming a general engineering manager, but being a small company, it required manager to be hands on and I did not have enough knowledge. So I was only the manager of EE all these years.
Also, another important thing, you don't need the right degree for your job. I never have an EE degree. Other than I got an AA degree in 9 months in the late 70s, I pretty much study everything on my own. I went far in my career doing heavy duty designs. I have seen people that were in the field differ from their degree. One common thing between these two you mentioned is Physics. A good physics background will give you a very strong start. I have seen PHDs of physics learning how do design electronics and mechanical things and did good jobs. I cannot speak for mechanical engineering. Electronics are not that hard. It only get hard when you get into EM and RF where most of it is Physics. A strong math will really help in either one. If you are good in Physics and math, you can read and learn electronics!
After almost 30 years, I still have passion in EE, now I am not working, I still study a lot. But instead of electronics, I spent the last six years studying ODE, PDE, EM and electrodynamics of physics major. I really feel I get a different insight in electronics and I can look at things in a different light. So back to you, you can study a lot of things before you even have to make the final decision.
Sorry I kept rambling on, I just feel there are more than just a major and I never have a chance to ask in forums in my days. I was just kind of blindly stumbling around all those years. All I know was I will never settle for second best. Believe me, in the late 70s, I got fired from my first field servicing job, my ex-wife's family encourage me to work in the restaurant because it was good money. I said no, and instead of looking for a job, I spent 3 months studying 18 hours a day 7 days a week to get into my first electronics job. They even threaten to take my ex-wife back!
