Words like "greatest" and other superlatives are more appropriate for a debate at a bar (or in fairness to White, a NY times bestseller) than an academic discussion of history. They are a harmless rhetorical flourish that doesn't contain much information.

The Vicksburg campaign is quite interesting to many military historians for a lot of reasons. It's quite complex, involving long distances, amphibious riverine operations, complex logistical problems, field battles, a siege, detailed planning and fluid improvisation. It's also decisive, breaking open the western theatre and putting the end of the war in sight.

However, the greatness or lack thereof is ultimately subjective. There are many ways to measure the performance of a general or an army and it would be quite easy to pick one in which Vickburg isn't "great" or even particularly surprising or unique.

If "greatness" then is subjective, statements of contemporary figures like Lincoln and Halleck are important because they show how the victory at Vicksburg provided Grant political leverage to assume high command and finish the war. The opinions of later military historians and authors are not quite as important and an extended discussion of "greatness" will become sterile, in the sense that it won't lead to much new information or understanding.