Usage of Auxiliary verb while comparing two prases

Hi

I am confused between the following two questions:



The decisions of John Marshall, the fourth chief justice, have had a greater influence than any chief justice in history.
(A) than any chief justice in history
(B) historically than any other chief justice
(C) than have those of any chief justice in history
(D) in history as any other chief justice has had
(E) than those of any other chief justice in history



The guiding principles of the tax plan released by the Treasury Department could have even a greater significance for the economy than the particulars of the plan.
(A) even a greater significance for the economy than
(B) a significance that is even greater for the economy than
(C) even greater significance for the economy than have
(D) even greater significance for the economy than do
(E) a significance even greater for the economy than have

OA in bold
My doubt is when to use an auxiliary verb such as 'have','do' and when to not to use them.
Why in the first sentence no auxiliary verb is required while in the second sentence it is required.