Hmm - interesting question... As I suspect you know, they all mean much the same thing - in this context. There is a slight difference - cardinal is not common, and is particularly used for more conceptual ideas, such as cardinal sin, and cardinal rule. Prime tends to be used similarly, such as prime reason. Although main and primary can be used in general terms, they are the only ones you would use in a technical sense, such as 'main water feed', and primary power source. Primary tends to be used where there is an implied secondary alternative.