Pros
It's great to work at a successful company, and Adobe has mastered the business it dominates in, namely creative professional software. You learn the ropes of the business from veterans, and you benefit from a playbook that's been working well for 20+ years. Strong culture of developing employees and a tightknit almost family atmosphere because of how long people have worked there.
Cons
As others have noted, because of the low turnover and strength of the employees, moving forward in your career can take a long, long time. I know one person I started with who got one bump up in level in eight years. They maintain a ratio for directors and above relative to individual contributors. Often easier to get a director title if you are recruited from outside the company.
