OK, I've tried to track down the Better one Rasputin than ten fits of hysterics original source. There is none directly to Nicholas II. It appeared in a 1922 piece called "Twilight of the Tsars" by one V.V. Shulgin, in an emigre publication (of Liberal, Monarchist Conservative politics), where it was cited as "a well known sentence of the Emperor's".
Prior, it appears in "The Minister of Evil The Secret History of RASPUTIN'S Betrayal of Russia" by William Le Queux, Cassell and Company, Ltd London, New York, Toronto and Melbourne First Published August 1918..
"Madame Vyrubova one day told me that the count (Freedericks) had that afternoon, in her presence, inquired of the Emperor:
Who is this new Starets of whom everybody is talking?"
"Oh! merely a simple mujik whose prayers carry right to Heaven," was His Majesty's answer. "He is endowed with most sublime faith."
The count then warned the Tsar of the displeasure which Rasputin's presence at Court was creating on every hand, adding:
"There are rumours that he is a mere drunken libertine. Make inquiries for yourself of his doings in Petrograd."
"Well, my dear Count," laughed the Emperor carelessly, "better one Starets than ten hysterics.", at pg 54.
NOW, here's the problem: Le Queux writes in the prologue "I received from the same sources in Russia a bulky manuscript upon very thin paper which contained certain confessions, revelations, and allegations made by its writer, FĂ©odor Rajevski, who acted as the mock-saint's secretary and body-servant" Well, we know, then that this is a HOAX document, why? because "Feodor Rjevski" wasn't Rasputin's secretary. His actual secretary was Aron Simanovich, who didn't publish his own book until 1921.
The real problem is that Orlando Figes quotes this as accurate, so does Greg King (in two books) and many other sources. This is a prime example of one writer not searching out the actual truth of the source, then it gets included into the "history" as "accurate". There is no first hand attribution to Nicholas II! Vyroubova never says it in her books. Freedericks never wrote it down...
I would, personally NOT place great faith in the accuracy. Amazing how stuff like this gets to become "factual" and "accurate"...