Have you considered the Applied Engineering Physics (AEP) major? It's the same as the normal physics major for the first four (or so) semesters, after which you diverge (specifically, AEP and physics take different upper division E&M and mechanics courses. Obviously the upper division electives are also different). If you don't know a specific type of engineering you want to go into, I would suggest this. Also, it's a happy compromise between full engineering and physics, since you walk the line between the two (and you can obviously take a lot of classes outside the strict set of applied engineering physics, such as astrophysics).
A general note about the atmosphere of the programs... The AEP students tend to be more competitive and grade focused than physics. For whatever reason, physics students are just content to learn the material and get what grades they get (A/A-/B+), but AEP people seem to stress much more about being at the top of the class, getting perfect marks, any curving, etc.