Pros
In my experiernce, BP employs truly quality people. I spent a summer there as an intern and was impressed with most of their employees. I worked as in intern within their supply chain department, and they gave me exposure to management at all structures and sought to give me a true view of the company while I was there.
Cons
They are a bit more old-school. There are definitely some 'gotchas' in their culture indicative that they don't have a full theory of the relationship between employee and employer. There are also rather rigid evaluation and promotion practices that seemed detriment. And there are definitely people there counting down the days until retirement, even people in their 30s. They also don't do a very good job of empowering employees. They are afraid of developing single points of failure and will intentionally limit what you are working on. The place moves at a crawl at times.