Pros
If set on getting a faculty job, one pro is that LBNL incentivizes academic behavior; i.e., publish basic science research. While postdocs cannot access career services at UC Berkeley, and career support services at LBNL were just cut, you can creatively leverage UCB to advance your career (e.g., recruiting events, networking with students). Senior management is trying to boost non-federal funding.
Cons
It is very important to understand how your prospective division and research group is funded, which may make the following generalizations more or less accurate. Consolidation of funds into large projects creates rigid hierarchies; pace is slow, like academia, diminishing the ability of young scientists to produce tangible results in a reasonable amount of time; because senior scientists have to pitch bigger and more ambitious ideas to DOE, projects increasingly focus on higher-risk, more complicated, and therefore less tangible work; you must be very careful that you have the right skill sets, given that imbalances between computer modeling and experimentation and physical technology development, and that the focus of funded projects can radically change within just 1 year. Much is made about LBNL being a meritocratic, soft-funded organization; in fact, most career/career-track scientists are effectively tenured, in that they migrate, sometimes outside their expertise, from completed or de-funded projects to funded projects. While these staff struggle, there is less support for younger staff.