Lets have a taste of History to understand the Market share Toyota holds currently.
First is Honda,
Company history
Soichiro Honda was a mechanic who, after working at Art Shokai, developed his own design for piston rings in 1938. He attempted to sell them to Toyota who rejected his first design. After two years of study and further refinement, Honda earned a contract from Toyota. He constructed a new facility to supply Toyota, but soon after, during World War II, the Honda piston manufacturing facilities were almost completely destroyed.
Soichiro Honda created a new company with what he had left in the Japanese market that was decimated by World War II; his country was starved of money and fuel, but still in need of basic transportation. Honda, utilizing his manufacturing facilities, attached an engine to a bicycle which created a cheap and efficient transport. He gave his company the name Honda Giken K?gy? Kabushiki Kaisha which translates to Honda Research Institute Company Ltd. Despite its grandiose name, the first facility bearing that name was a simple wooden shack where Mr. Honda and his associates would fit the engines to bicycles. The official Japanese name for Honda Motor Company Ltd. remains the same in honor of Soichiro Honda's efforts. On 24 September 1948 the Honda Motor Co. was officially founded in Japan.
Now Toyota,
Company history
The Toyota Motor Corporation was founded in September 1933 when Toyoda Automatic Loom created a new division devoted to the production of automobiles under the direction of the founder's son, Kiichiro Toyoda. Soon thereafter, the division produced its first Type A Engine in 1934, which was used in the first Model A1 passenger car in May 1935 and the G1 truck in August 1935. Production of the Model AA passenger car started in 1936. Early vehicles bear a striking resemblance to the Dodge Power Wagon and Chevrolet, with some parts actually interchanging with their American originals.
Although the Toyota Group is best known today for its cars, it is still in the textile business and still makes automatic looms, which are now fully computerized, and electric sewing machines which are available worldwide.
Toyota Motor Co. was established as an independent company in 1937. Although the founding family name is Toyoda, the company name was changed in order to signify the separation of the founders' work life from home life, to simplify the pronunciation, and to give the company a happy beginning. Toyota is considered luckier than Toyoda in Japan, where eight is regarded as a lucky number, and eight is the number of strokes it takes to write Toyota in Katakana. In Chinese, the company and its vehicles are still referred to by the equivalent characters, with Chinese reading.
source :- http://en.wikipedia.org/
The big brother thus dominates! But people we here are not discussing who dominates the industry, which is quiet obvious, BUT Which Company is at the peak of Engine Technology and Performance + Economy. :)
