The difference between Lauryl- and Cocoyl-products is more pronounce when the surfactants are not blended and used as the only surfactant. Most consumer products are blends and the final effects and sensorials will likely be the same (or only slightly different) when replacing one for the other.
In general, it seems that people prefer cocoyl-products because they are slightly milder on skin.
Because lauryl-glycerides are the major component of coconut oils, then your cocoyl-surfactant will always lie pretty close to the lauryl-surfactant in therms of properties. Deviations are imparted by the relative ratio between the lauric-fraction and the capric/caprylic and palmitic/stearic/oleic fractions.
One possible additional factor to consider is defined by the industry standards (see Perry’s post). Thanks to that, you can always rely on Lauryl-surfactants to behave the same way in every formulation (including their native pH). Cocoyl-surfactants will have slightly different properties across different producers, depending on their sources of oils / manufacturing process (including their native pH, which might require different adjustment at the end of your formulation process).
Then, there is the marketing effect of saying something is derived from Coconut, or otherwise naturally derived.
I think Lauric acid / Lauric alcohol are still produced largely from vegetable sources (perhaps 25-35% is produced from petrochemicals). So, if you source your Lauryl-surfactant manufacturer properly you can claim that as well.
In my own view, the only difference here would be “how green is my surfactant?” Using Cocoyl-based, means that I didn’t have to purify the Lauric fraction from the others (usually done by fractional distillation of esters or alcohols, which is an energy intensive process). But this opens up for another can of worms.