Pros
Hands down, no other company (or government for that matter) is pushing the boundaries of space exploration and access at the same rate that SpaceX is. I work here because I believe that I can personally have the largest possible positive impact on the world by spending my time and energy supporting SpaceX's mission. There is a real and widespread sense of the importance and impactfulness of what we're doing, and everyone, management to new hires, bring an urgency and drive to their projects that is unmatched anywhere else I know of. Individual contributors are given a huge amount of responsibility and can make significant contributions to big projects and milestones on an accelerated timeline with minimal bureaucracy.
Cons
Responsibility is a double edge sword, and the drive for extreme ownership and personal responsibility can be very stressful at times, and very rewarding at others. SpaceX can also quickly take over large swaths of your free time as you find yourself working long hours - it's important to set clear personal work/life boundaries for yourself here, and make sure you work at a pace that is sustainable for you. Other people and management won't do that for you at SpaceX, and people occasionally fail to find that correct balance for themselves and burn out.