Pros
BP pays well for the work that you do. They have one of the best benefits packages that I've seen. When they are making money they like to spend it and bonuses almost always get paid.
Cons
BP is a poorly managed company, their safety track record speaks for itself. Though they advertise that they are focused on improving, leadership has done little to change the culture. They've been in constant "transformation" for the last 5-8 years. Also just recently, at least in the US they have been making it more challenging to participate in agile working arrangements. Leadership has not eliminated agile working, they have just communicated a message that does not promote it. Because they pay well senior managers tend not to leave, and most are waiting for a severance package to do so. This leads to very little long term opportunity.