My 2 (or more) cents: research roles in industry and research roles in government/academia usually are pretty different. Some people like both, some people are really turned off by the pacing and challenges of one or the other.
I personally lean much stronger in the government/academia direction. However, the pacing and daily life in that kind of setting was still a lot different than what I thought it would be like in high school and even in college where I gained some research experience. The constant demands of obtaining grants and publishing papers is something that can be overlooked, even as an undergraduate researcher. Particularly, obtaining funding can feel like an albatross around your neck in some situations. In addition to that, there are lot of meetings, conference calls, power point presentations, and sitting at a computer. All in all, quite a lot of 'politics' and non-science stuff going on that was unexpected. In fact, graduate school was when I first really started paying attention to federal budget issues, not only because I had matured as a person, but because it directly impacted my career.
I'm not going to say I didn't enjoy it. I did a lot. I loved going to conferences and interacting with new and old acquaintances - heck, going to conferences and hanging out with my friends that I saw twice a year was possibly one of the biggest perks. I also enjoyed going to Washington DC to lobby for my field and traveling to give talks, and lots of the other non-research stuff. I could do without some of the meetings :) But it was different from what I expected.
I think some of this feel can be had in industry depending on what you end up working on and who you are working for. Startups or established companies that are large enough to have a sizable R&D wing, etc. Medical imaging for example; I think if you work for one of the large suppliers of advanced medical diagnostics like PET or MRI machines, you could be involved in some pretty cutting edge work. You will probably need a Ph.D. to be involved in a lot of that type of work. You will also need to be careful of what kind of physics you end up practicing. Medical physics or nuclear physics might be a good start if you want to get into the medical imaging field. Heck, even plasma physics (my field) might be acceptable IF you worked on the right type of research (some stuff uses a lot of tomographic techniques).
It's a bit of knee jerk reaction, but I would think if that's the kind of stuff you want to do AND you wanted to do engineering, EE is probably a wiser choice than mechanical.
As to whether or not there's a lot of competition, I'm getting cynical in my old age. It's looking to me that pretty much any field you go into is going to be a rat race. I won't discourage anyone from getting their Ph.D. in hopes of being a professor or research; I WILL tell them that it won't be easy and there's a high likelihood that you won't end up doing what you planned on. But that's true of most of my friends from college and high school, no matter what their aspirations were.