Pros
For Process Engineering, there is a much more tried and true path. Doors open for Process Engineers in a way that they don't necessarily for other disciplines. There is also opportunity for mobility within disciplines. While the world of upstream (exploration and production) and downstream (refining and marketing) are fairly segregated, there is a lot of opportunity within those, but it's definitely a function of how broad your network is (and whether or not you have others endorsing you).
Cons
The company operates in a very reactive manner (and considering there are shattering incidents that seem to occur every so often, that's not a good thing). Currently, oil price is down, and there are job cuts all around (the jobs that were added - but were they necessary? - back when the going was good and crude was high). When the going gets good again, the projects will commence and there will be an influx. While this is normal in any cyclical industry, there are ways to manage this in teams/roles that are justified ALL the time - and don't just come and go, based on financial performance. This company loves reorganizing and restructuring. The message can be all about alternative energy and environmental compliance one day, and then shift to process safety solely the other - there isn't a balance across all to systematically oversee the entire portfolio through ANY type of market. Similarly, when I first joined (6.5 years ago), the company was open to moving cross-functionally, as long as you were eager to learn and could prove yourself. Now, there is a significant shift toward specialization, and keeping people in their current track. Also, my experience has taught me that proving yourself as a high performer, when early in your career, can sometimes be a double-edged sword. Management won't want to get rid of you, and just keep you in your role.