I think Einstein was more influential, since he changed the fundamental way we understand how everything in the universe works.

Also, while Turing made very important contributions to the fundamentals of computer science, there were others who were working on similar models of computability, such as Alonzo Church. I have great admiration for Turing (especially after having read his biography by Hodges[1]), but I think that if Turing had never come along, we'd still have computers and computer science today.

Turing's most influential work may have been his wartime cryptanalysis, which may have been pivotal in the Allies' victory in WWII. On the other hand, Einstein (and others) urged President Roosevelt to develop nuclear weapons before the Germans did, which certainly influenced today's world in significant ways.

[1] https://www.amazon.com/dp/069116472X

Another mistake, which had serious consequences to the Germans, was that a German weather ship in the North Atlantic accidentally transmitted their weather report using the Enigma key reserved for naval operations rather than the key used for routine information, noticed the mistake, and then immediately retransmitted the identical message using the routine key. Since weather forecasts have predictable content and format (and are thus easier to decrypt), this error allowed the Bletchley Park people to crack the operations key much more quickly than they otherwise could have.

This episode is described in the book Alan Turing: The Enigma[1], which was the basis for "The Imitation Game" film. I highly recommend this book if you're interested in Turing, cryptography, or the early days of computing. While Turing is best known today for his work on the theoretical underpinnings of computer science (due to the Turing Machine that bears his name), he also worked on the design of one of the early general purpose computers (the ACE[2]) after the war, on voice encryption hardware, and other interesting stuff.

[1] http://www.amazon.com/Alan-Turing-Enigma-Inspired-Imitation/...

[2] https://en.wikipedia.org/wiki/Automatic_Computing_Engine

My recommendation when anyone asks this.

1. Alan Turing: The Enigma by Andrew Hodges http://www.amazon.com/Alan-Turing-Enigma-Inspired-Imitation/...

Definitive and detailed biography.

2. Alan M. Turing by Sara Turing http://www.amazon.com/Alan-M-Turing-Centenary-Edition/dp/110...

Deeply personal biography of her dead son.

3. The Annotated Turing by Charles Petzold http://www.amazon.com/Annotated-Turing-Through-Historic-Comp...

Turing's famous 1936 explained in detail.

The author seems to have linked to the wrong book as the inspiration for the movie though the author's name is correct.

This is the book I remember seeing named in the credits: http://www.amazon.com/Alan-Turing-Enigma-Inspired-Imitation-...

I don't care that I'm beating a dead horse here - if you haven't read Andrew Hodges' excellent biography of Alan Turing, you should put it on your holiday reading list. Link: http://www.amazon.com/Alan-Turing-Enigma-Inspired-Imitation/...