Google receives 3.5bn daily searches, Facebook receives 1.5bn

"Each day, Facebook handles 1.5 billion searches against the 2 trillion posts in its index. They’re still a ways off from Google’s 3.5 billion daily searches, but it’s an impressive figure nonetheless and puts Facebook right up there as far as search giants go.
Of course, Facebook is only indexing content within its own ecosystem, while Google, Bing, Yahoo and the like make much of the web’s content available to searchers."

Source:  Larry Kim on Medium, 26th October 2015

Facebook stat - Facebook, 22nd Oct 2015

Google stat - Internet Live Stats - no official figures from Google