It depends what type of person you are because they require two very different skill sets.
Structural engineering will require a lot of calculations and pencil pushing. You will often be performing calcs involving statics and the mechanics of materials. There is also a TON of corporate office bureaucracy and it will drive you mental at times. You will mostly have regular work hours and your office should be in a large city. Ultimately, you will get to decide "what" gets built.
Construction management will require a lot of hand-holding and cat-herding. The position has a bit longer and erratic work hours; you may be tethered to your cell phone. There is also a lot of office bullshit they always seem to get around a lot of it. Depending on what type of project it is, the construction manager could either be trying to save the client money, or trying to make the contractor rich. It's a messy game in that sense. You could also be sent to a site in the middle of nowhere. Ultimately, you will decide "how" it gets built.
So what do you want to do? What do you prefer? Working with numbers or working with people?
Feel free to write