General Electronics vs. Embedded programming oriented program
Obviously my answer is based on my personal experience. Your mileage may vary. A little background: I double-majored in computer science and computer engineering. At the time, my CpE program was more like a hybrid between the programs you describe, but since then it's transitioned into separate tracks. I've observed students, both in class and graduates, each year since I graduated. I work at an OEM, primarily as an embedded systems designer, but I'm branching out into power work.

My biggest educational regret is that I didn't have a chance to take the more solidly EE courses, like electromagnetic fields, control systems, power systems analysis, and power electronics. All that would have made my career much smoother. Similarly, seeing other graduates who had even less of the electrical side than I did, they're even less prepared. You may be able to program all day long, but if you don't know what an op amp is, or how to drive a FET to invert logic, you're always going to be at the mercy of other designers. You'll need them to be useful, and you'll have much more difficulty integrating yourself into your company. Your career options will be more limited, and you'll be in a constant state of, if not confusion, than at least constant awareness of your own limits.

You're always better off understanding the context you operate in. Working at an OEM, the biggest limitation on my capabilities now is that I don't have a firm grasp of integration-level work. Who buys our stuff and what they do with it, I'm still shaky on, and it hurts my abilities as an engineer. Similarly, an embedded systems programmer who doesn't understand what goes on past the pins of his processor is going to have a much larger learning curve than a general electrical engineer with some programming background that tries to do the same job.