@mikey_mike. I totally agree, which is why I qualified my first sentence with the rider “in natural habitat”. I don’t doubt within an urban landscape that Cresteds and Spotteds compete for certain common food resources. The fact that Cresteds have been able to invade and establish themselves in a city the size of Sydney says they are able to utilise a substantial variety of the seed resources available in urban areas. Crested pigeons are fairly good at driving off other species and I suspect that, depending on the particular situation, such as the range and degree of resources available, sometimes they hold their own against Spotted Doves and sometimes they don’t.
The Rock Doves that you mention at Rockingham are still urban animals. They are competing with natives within the metropolitan area. This is true of other urban established invaders like the Common Myna, which competes with native birds.