How far are you currently in college? Because I'm going into my third year of studying as an ME and it's pretty tough. I have friend's who are in EE and they say it's not any easier. I mean engineering is a tough major all together but if you can handle it than by all means go for it. At the same time just make sure you don't bite off more than you can chew, because a dual degree in engineering is tough.
Also, some things look good on paper, but when it comes to practicality it's not really worth it. If you get an ME degree and work a job that requires EE skills, chances are if they hired you, you'll learn those skills on the job. Same goes for vice versa. I know a guy who was in charge of making programs to run nuclear reactors at the power plant he worked at. He graduated with a PhD in ME. He had neither a nuclear engineering degree nor a computer science degree, but they taught him all of the stuff he needed to know after he got the job. So for now I say just go for whatever you really think interests you the most, you'll learn the other stuff along the way.