What is most desirable is what you like. I like canted corners in Asscher cuts - almost to the point of GIA defining them as octagonal step cut, rather than square emerald cut, and this is the more traditional aspect for an Asscher. Others prefer a "fuller" look.
This said, the one sizeable Asscher I have is almost completely the opposite of a traditional Asscher, with relatively full corners and a large-ish table, but it had the look I wanted for a certain project.
If by "brilliance" you mean the amount of light reflected, the extent to which the corners are cut will have a minor impact; what matters most are the pavilion angles, particularly of the first and second tier of pavilion facets. "Of course", this is not information that is available through a report, so choose a vendor who can help you by seeing, selecting and taking good photos of the best cut diamonds, rather than buying "off a list" where the information available is insufficient to make a decision.