Every project is different, and quite often requires using different software to accomplish. In the most part Adobe Photoshop is used to create any rough concept work and visuals. Form this the final artwork is then either finished in Photoshop or taken into Adobe Illustrator to create neater lines. It all depends on the look and feel required for the final artwork. When creating animations, the initial process is the same for artwork, but then taken into Animation software.
When animating, software such as Toon Boom Harmony, Adobe After Effects and Apple Motion are utilised with all final video editing done in Final Cut Pro.