I do not understand how you can conclude that they both are even competitors - along any dimension

Perplexity has now become a speciality tool used for a few use cases primarily via third party models (unsure if they are still continuing to develop their own mdoels and where they rank)

Google on the other hand is still actively trying to develop SOTA models (or at least 3rd best) and also is widely used amongst cost sensitive projects.

I see no comparison between them worth putting them alongside each other.