What was meant by the wider variety is due to the Cameo and the first wide bed. I am not familiar with the overall production numbers but I am fairly sure that Ford had the lion share of the market until 1955 maybe 56.
Chevrolet was the USA national truck sales leader in all Advance-Design years.
Chevrolet trucks continued this market dominance in all Task Force years.
Chevolet remained the truck sales leader through at least 1972.