Is Affinity Photo faster than Photoshop? Not always. Most of the filters in Affinity Photo are faster and the software uses significantly less RAM and VRAM. Affinity Photo also has some tricks up its sleeve to make the interface "feel" snappier (not actually faster).
Photoshop still excels at things like the Camera Raw Editor which is way faster and smoother than Affinity Photo's Develop Persona. Photoshop's startup time is also faster by a couple seconds.
On slower computers with 4GB of RAM or less, Affinity Photo will feel faster because it uses less resources. On faster computers with 8GB of RAM or more, the performance benefit Affinity Photo has is minimal and should not be the deciding factor for choosing Affinity Photo. Instead, you should be looking at things like features, pricing, and how it fits your workflow.
To learn more about the differences, watch our Affinity Photo vs Photoshop review.