The web site by Dr Harry Bhadeshia with the University of Cambridge contains lecture notes on martensite transformation. He is probably the foremost expert on martensite and bainite transformations in steels. In one of his lectures, he states that lath (dislocation) and plate (twinning) induced martensite formation on cooling is a function of martensite start (Ms) temperature - which by the way is influenced by various alloying elements, most notably carbon content. He reports that for every 1% increase in carbon content, the Ms temperature of steel decreases by 470 deg C.
To summarize, the formation of lath martensite upon cooling is favored for steels exhibiting high Ms temperatures, whereas steels that exhibit low Ms temperature tend to favor plate (twinned) martensite. Martensite phase transformation in steels is driven by temperature differential upon cooling, thus producing a displacement of atom planes that physically strains the original (austenite phase) lattice or crystal structure of the metal. There is no diffusion of atoms during the formation of martensite from austenite. Thus, the greater the temperature differential upon cooling, the greater the tendency to form plates (twinning) versus laths to accommodate these lattice strains.
So to answer your question, and using the above information, the higher the carbon content in steel, the lower the Ms temperature, thus favoring the tendency to form plate martensite versus lath martensite.
There is another good source of information on martensite transformation of steels in the "Physical Metallurgy Handbook" by Anhil Sinha.
