Higher is more typically used when there is some kind of scale or chart or list -- higher taxes, higher salary, higher education. Greater is more often used of things that lack that measure -- greater freedom, greater responsibility. There are many situations where they are interchangeable -- greater/higher compensation,a greater/higher power, greater/higher cost.

Well explained by Jim . For me Higher/Lower is bit of VERTICAL , eg - higher volume , higher intensity , higher salary etc and Greater is bit of HORIZONTAL. If u dn't get a clue of this silly concept just forget it , its my way of keeping it clear.

Here goes an example from official source with the concept :-

In addition to having more protein -than wheat does, the protein in rice is higher quality than that in wheat, with more of the amino acids essential to the human diet.
(A) the protein in rice is higher quality than that in
(B) rice has protein of higher quality than that in
(C) the protein in rice is higher in quality than it is in
(D) rice protein is higher in quality than it is in
(E) rice has a protein higher in quality than

OA B

Sorry for the typo .

AIM GMAT wrote:Well explained by Jim . For me Higher/Lower is bit of VERTICAL , eg - higher volume , higher intensity , higher salary etc and Greater is bit of HORIZONTAL. If u dn't get a clue of this silly concept just forget it , its my way of keeping it clear.

Here goes an example from official source with the concept :-

In addition to having more protein -than wheat does, the protein in rice is higher quality than that in wheat, with more of the amino acids essential to the human diet.
(A) the protein in rice is higher quality than that in
(B) rice has protein of higher quality than that in
(C) the protein in rice is higher in quality than it is in
(D) rice protein is higher in quality than it is in
(E) rice has a protein higher in quality than

OA A

In addition to having more protein --what it is modifying? Rice
So A,C,D out
We are left with B/E

E is making wrong comparison between protein in rice and wheat.
We need that in (in B) to make comparison clear.

So IMO B

OA please !!!

OA is B .