Avantages
To be honest I cant think of any "best reasons" other than that it's a fairly recognizable name so it would generally look good on a resume, depending on what you want to go into. I did generally like the people on my project - a rarity being a somewhat female-dominated project in a developing country. But I'm not sure how much that had to do with BE itself, as a lot of them were contractors who have since upped and left. Oh actually, here's one good reason: it seems at least the people I know are generally pretty satisfied with their work-life balance. I had a pretty regular 9 to 5 schedule and so do some colleagues on entirely different domestic projects.
Inconvénients
Virtually no job stability. If you ever end up on the bench for more than 3 weeks you're pretty much screwed. Many people always felt that they needed to be actively looking or have a backup job somewhere. BE will treat you like a corporate cog no matter how well you perform - though probably about as much as any large corporation will.