Aero programs are vastly different based on where you go:
In my program (I'm in the last undergrad semester at University of Maryland), there are two tracks: aeronautical and space systems.
Up until the second semester of Junior year everyone takes the same classes:
Calculus I,II,MV
Differential Equations
Physics I,II,III
Statics, Dynamics
Thermodynamics
AFAIK, those are the same for practically every engineering except maybe for EE (the statics, dynamics, and thermo).
all AE students http://www.enae.umd.edu/department/undergrad/
Intro to aerodynamics (taken 2nd sem. sophomore year) which covers a primer to thermo and its applications to aerodynamics, incompressible flow, introductory airplane performance, and a smattering of rocketry stuff.
Aerodynamics I (taken 1st sem. Junior year) covers supersonic flow and flow through nozzles
Dynamics of aerospace systems (1st Junior): goes into more detail of dynamics including quaternions and other 3-d applications
Aerospace structures (2nd Junior): goes into the layout and sizing of wing boxes, fuselages, etc
Control systems (2nd Junior): the hardest class I have been into date, covers, well... control systems.
Vibration & aeroelasticity (1st senior): various vibration topics and wing bending and dynamics
Two lab courses (1st Junior and 2nd senior)
In addition, the aero-heads take aerodynamics 2 which covers subsonic flow, aircraft flight dynamics, aircraft propulsion & power (ramjets, props, etc.), principles of aircraft design (intro design class... they designed a jet airliner last semester is all I know), aeronautical system design (builds on the intro class).
Space-cadets (myself included) take spaceflight dynamics (satellites, orbital maneuvering, etc... cool stuff), space propulsion & power (solid, liquid, hybrid, electric, a little nuclear... believe it or not one of the easier classes I've had), space navigation & guidance (a misnomer... actually we learned what our spaceflight dynamics professor does for a living... satellite monitoring, etc. Really boring and tedious stuff), Principles of space system design (the hardest class you'll ever enjoy, taught by the professor who coined my quote... researched one launch vehicle, designed an orbital space plane in a team of four over two months), and space systems design which I'm slogging through right now... also taught by Akin, the whole class is the team, broken up into disciplines; design a spacecraft /mission from scratch over the duration of the semester.
For the mechanical engineering degree, you get a whole lot more flexibility into what classes you can take. http://www.enme.umd.edu/undergraduate/courses/electives.html is their listing (probably not complete).
If you're somewhat interrested in space stuff as a mechie, you could probably take some fluids courses and get hired to design rockets or some robotics courses to design landers/rovers. You'll be missing out on being well rounded in space type apps. For aeronautical apps, you'd be better off in the AE dept. You won't get the full range as an ME. The other side of the coin, of course, is that you'll be able to find a job in a wider range of companies when you graduate.
Oh... and you won't have much of a social life regardless of which major you pick. For me this semester I spend more 12+ hour days in the lab than I care to think about (hence my location).