First of all, the most important thing is to look at the courses required for each major you are thinking about, and see if you have any sense of which looks more appealing. But that can be difficult to judge coming out of high school, as everything may look unfamiliar.
If you're wondering about this from an enjoyment perspective only, there are a number of things going against engineering. At most universities, engineering will probably have significantly more course requirements than physics (or pretty much any other major). This is because engineering programs are accredited, and need to cover a large number of subjects which are considered important, even if those subjects aren't important for you as an individual.
I did materials engineering as an undergrad, and I had to take a number of courses which I thought were useless because of this reason. For example, I had a thermodynamics class which was all about turbines, heat exchangers, using steam tables, looking up thermodynamic data, etc. It didn't teach the fundamentals of thermodynamics in any satisfactory way. That's probably typical of many intro thermo classes in engineering, but to me it is a waste of time. From my perspective, if you have a thorough understanding of the laws of thermo and the way the various thermodynamic potentials are defined and used, you will be well equipped to figure out how a turbine works or use a steam table later on, should you need to do that.
There were other situations in engineering where I felt that courses weren't providing me with any fundamentally new information. For example, I had one on processing of electronic materials. It seemed more like a superficial survey of topics from solid state physics and other areas of physics, applied to integrated circuit design and processing. Again, the theme is the same. If you have a deep understanding of the physics, you should be able to read about materials processing and (almost) immediately understand the important concepts. But because I was taking classes like this, I didn't have a chance to take a real solid state course.
Particularly if you go to grad school, the main value of your undergrad degree will be how much it helps you in learning new concepts, because chances are, whatever you end up working on will be something you haven't learned yet. Either physics or engineering will provide you with the necessary problem solving skills, calculus, differential equations, and basic scientific intuition needed to approach new topics. However, the hardest situation for self-teaching is when there is an entire formalism you never learned about, for example Lagrangian or Hamiltonian mechanics, or relativity. This is the situation I'm in now. I'd love to learn about these things from the perspective of interest, but they only come up peripherally in my area, and it's hard to justify the time it would take me to learn them.
Also, since physics will probably leave you with more choices for your classes, you will be free to take a few engineering courses on the side if there are topics you find are missing from the physics curriculum.It may seem like I'm totally pushing for physics, but that's just because that's what I would have chosen. If you think you are more interested in learning how man-made systems function, or how to design things, by all means, choose engineering.P.S. Since your question is "will I enjoy engineering" I would say that yes, you probably will. At the core, it's still science and you will cover a ton of interesting things. It's just the overall emphasis that may or may not suit you. I still ENJOYED my degree, I just think I would have enjoyed physics even more.
