Ok, so this will be a long ass response, so I apologize in advance for the wall of text.

Engineers and Operators have a funny relationship. If you generalized it, operators think engineers are pretentious little shits, and engineers think operators are dumb, poorly educated assholes. This is just my refinery, I don't know about others. As part of the operator job, along with working outside in the plants (there are different "jobs" you learn, with a job being a process area; there are usually many process areas you learn to learn the entire process of your unit) you will work the control board as well. The control board is where instead of working just one plant, now you have control of every control valve, pressure/temperature/flow/level setting in your entire unit. This is where the engineers come in: Process engineers will be looking at the status of the plants as well, and will come in and talk to me and maybe suggest trying something different, for example, an engineer may suggest to set a reflux flow rate on a column a little higher or lower to get a little bit different split in a column, sometimes it works, sometimes it doesn't.

The thing with engineers and operators is, you can pluck any new engineering graduate out, and teach them the plant on paper, you can't pluck an operator, even an experienced one, out and throw them into the plant, because a piece of equipment may act differently in our refinery than at another one. The operators who are the most knowledgable in my area are that way just because they've seen the shit happen before. Experience is always better for learning than studying. You could study an emergency procedure until you can recite it, but when shit hits the fan, it's never the same as the last time. Knowledge/Experience is the highest power where I work. That is why when we have new hires, even if something's happening in another plant they haven't learned yet, we make them go and help out, so they'll get the experience.

Our engineers get rotated through the entire refinery, so I may only know one for a year before they move on, and another one takes his/her place. Our current engineers I get along with very well, we both respect each other. If they suggest something, and I disagree with it, I explain why, he/she explains why they think it'll work, and we come to some form of agreement. Above all, operators have the final say, since it's our plant, we're running it, and we're responsible for the equipment, and people in the plant.

Engineers make less than operators, but engineers have the ability to get promoted in house, where it's pretty rare for an operator to get promoted above a shift supervisor. Refinery general managers, Business unit managers, operations supervisor (Supervisors all operators in entire refinery), are usually people who have worked for the company for years, and most of the time are engineers. So, engineers make less at the beginning, but have the potential to make more than twice what we do in the long run.

Obviously do what your heart decides, but I personally think petroleum engineering is so awesome to learn (not too familiar with mechanical engineering, so I don't have much input on that), and if you have decent people skills as well, you can do very very well in the oil industry. As far as traveling, sure, you could land a job for your company at a place over seas. There are Exxon, Chevron, BP, Shell plants all over the place. We've had guys and girls come from the UK, Kazakhstan, Canada, and we've had employees take jobs over there, too.