phys natsci or engineering for careers

Was just wondering if any of these degrees has a recognisable advantage over the other in employment opportunities in fields like quant or any field for that matter. How does the maths in each subject differ; is the maths in phys natsci, if you took the physics options, more rigorous/difficult than engineering. lastly, is a career in space travel/rocket engineering a common career path and is it well paid?