Math in ComputingMechanical and Electronic Calculating Devices 
Has there ever been a competition

Yes, there was once a competition between someone using a calculator and another person using an abacus. Although the abacus is often considered a “crude” device to do simple calculations, in expert hands it can work just about as fast as a calculator.
The contest took place in Tokyo, Japan, on November 12, 1946, between the Japanese abacus and an electric calculating machine. The event was sponsored by the U.S. Army newspaper Stars and Stripes. The American working the calculating machine was Private Thomas Nathan Wood of the 20th Finance Disbursing Section (from General MacArthur’s headquarters), who was considered an expert calculator operator. The Japanese chose Kiyoshi Matsuzaki, himself an expert operator of the abacus, from the Savings Bureau of the Ministry of Postal Administration. In the end, the 2,000yearold abacus beat the electric calculating machine in adding, subtracting, dividing, and a problem including all three with multiplication thrown in. The machine only won when it came to problems in multiplication.