Pros
Seriously good company to work for. A lot of opportunities to grow in your career if you know how to steer it. Very international environment, exposure to interesting projects, possibility to travel the world, work with people from different countries and cultures. Reasonable and flexible work-life balance, great benefits. If you chose an international mobile career be prepared to lots of travel and moving residence every 3 years. They give you a lot of training during your career so you evolve quick. On-boarding for new hires is well done.
Cons
As soon as oil prices deep below certain value, first thing this company does is it quickly cuts overhead costs. Everyone's job becomes vulnerable, even being a "high potential" or high performer in your team does not guaranty job security when things get hot. This company known to shed 10-25% of its workforce easily. However with Schlumberger experience it should be not a problem to find another job fairly soon elsewhere.