Engineering schools are generally more selective. The classes that are taught just to engineering students are at a higher level. If your daughter is as well prepared as she sounds, I would recommend going the engineering route.
CS in a general studies curriculum will involve (and I speak only from my personal experience) more “business-applicable” courses. You’re not likely to study compilers in CS, but you will know your way around a pivot table.
If your daughter wants to build computers or robotics, or go into teaching – Engineering.
Honestly, neither is a bad choice, but if you are looking to be employable right out of school, I would say CS. Anything from a “liberal arts” background (despite what you may have heard) will give your daughter the ability to do more than just design a circuit.