Pros
The best reason to work for Exxon is stability. For the permanent employees there is not a significant risk of being laid off even in an economic downturn. If you are picked as one of the "golden children" (which not many are) there is a monetary reward in that your salary will far out pace your peers. There are opprotunites to work outside of the US for someone who wants to see the world. There is an advantage a good support structure for young employees to learn quickly from many mentors (but in about five years almost all those mentors are going to retire).
Cons
There are downsides to working for any large corporation but they are blatantly clear in Exxon. The corporation is very slow change to meet the changing priorities of the younger employees. A forced ranking system is in effect for all professional employees which breeds discontent as even if an employee is performing at a very high level the employee can still be ranked at the very bottom....and being ranked at the very bottom means that salary increases are less and less frequent. As far as I can tell, people in the bottom 20% get raises about every 20 - 22 months at the rate of of inflation if not less. The company does not offer an alternate work schedule and management will not even entertain the idea for their professional employees. The overall culture of Exxon breeds managers who place morale very low on the priority list and treats the employees as if they were interchangable with anyone off the street. There also does not seem to be any clue about family and work balance. If by chance a people friendly manager does come about that person typically ends up in low middle management and does not go farther than that.