Pros
Great benefits and career opportunities. Offers stock options and has a high dividend compared to its competitors. Plenty of opportunities to work capital projects, develop fields, or optimize production, both internationally and domestic. They also offer copious amounts of career training and are very safety conscious.
Cons
There can sometimes be too much red tape in order to get approval for projects, even the low cost projects. This leads to delays and makes an engineer spin his wheels. Also, because they are so safety conscious, there tends to be problems with project costs. From an employee perspective, they care more about their investors than their employees (as seen from them refusing to cut their "highest paying dividend").