My bachelors and masters are in mechanical engineering (my PhD--which I'm now pursuing--is in engineering mechanics--and yes, there is a difference).
The two fields EE and ME are different in course material (extremely different), but require a similar kind of mindset. A lot of the same math, physics, and sciences... but the "major" courses are wholly different.
As far as working on "cars and stuff", mechanical engineers do a LOT more than that. That's like saying an electrical engineer works on transformers.

The fundamentals of mechanical engineering have to do with the motion of any body, the stresses and strains in a body, and of course, thermodynamics (the motion of heat, if you will). So, MEs have a variety of jobs. In fact, a LOT of the new jobs in the micro-electronics industry are for MEs and material scientists.... how do you think these things get made? In fact, my masters thesis was working on the shaping/tailoring of hard disk heads to reduce fly height--thus allowing higher data densities and faster read speeds.
I suggest you go talk to the department at your school.... see what kind of work UNDERGRADUATES do. See which one interests you more. And don't make any "quick" conclusions--like EEs work with computers and MEs are greasemonkeys and work on cars--you'll see all different kinds of things done in the departments (and you'll find that a term like "electrical engineer" is a broad one).
Best of luck.