It is not either/or. Personally I would use both, or use Photoshop and Illustrator so you need to know how to work in these three effectively. These three apps are the normal everyday tools of the graphic designer. If this work was intended ONLY for web site/social media though (not print) I might use only Photoshop because the amount of text is small and almost all large titling. But the small type suggests it was not designed for screen delivery.