Avantages
Total autonomy. Adobe really believes in the freedom to work how you work best. It is refreshing to see a company hire talent and then offer an environment where they can contribute freely. Lots of cool perks across the board. Great worldwide HQ campus. Really focused on being environmentally conscious, and of course who can forget free access to everything produced by Adobe. They even have a system for you to buy retail packaged software for your friends/family at a ridiculously discounted rate.
Inconvénients
It's a big company so it can sometimes seem difficult to plot your career advancement, though they do offer help in this respect. I've heard of others taking up the offer to move around departments/roles, but honestly I think this is primarily geared at the most junior level employees. The reality is, they hire top talent and understandably want to see the fruits of their recruitment in a specific area they tapped you for.