Personally, I'd stick with physics as I found it more intellectually satisfying. Engineering by its nature is limited because it's about the practical application of science and math to build something. Some people like to design and build things. If that's you, engineering might be a better choice.
The main advantage of an engineering degree is that it makes it easier to get an entry-level engineering job. Having a BS in physics, however, will qualify you for many of those same jobs. It's just that you won't get the automatic pass on the first cut that the phrase "engineering major" on your application or resume will afford you. The advantage of physics is that it's more general and wide-ranging. It's easier to go from physics and specialize in engineering than the other way around, if you later realize you chose wrong.
Also, you should realize there's a wide range of engineering jobs. Most engineering majors aren't going to get designing jobs right out of college. A lot will be hired to provide application support, to do testing and quality assurance, etc. A lot of these position you can do with a BS in physics. The main obstacle is getting the hiring people to consider you in the first place.
Have you discussed your options with the professors you work with? The department should have some interest in making sure its graduates can find good employment if they choose not to go to graduate school. They can probably give you a better idea of what your outlook after graduation looks like and might even be able to help you find a good position.
Can you do a minor in engineering or simply take engineering courses on the side? I'd start with that, and if you find you really prefer engineering over physics, then consider changing majors. I wouldn't change majors simply because you think majoring in engineering is going to get you a job more easily.