I feel both the tools Photoshop and Illustrator are the best tools for graphic designing. But with many new tools in the market you can try the best one.
There is much graphic design software available but I think the best software for graphic design is Blender. It is the best free 3D animation software. There are so many features of this software like it is basically design for the 3D applications. It provides amazing key frame animation tool. This tool is including modifiers, textures and simulation tool etc.