Use the word "higher" or "more" when referring to costs?

Is it proper to say that "the cost of X is more than the cost of Y" or "the cost of X is higher than the cost of Y"? Or are they interchangeable?

June Casagrande covers this one in Grammar Snobs Are Great Big Meanies. The answer depends on the usage of "cost". If the noun in question is a number then "greater" is correct. Cost can refer to a number depending upon what X and Y are. For example, "The cost of a Harvard education is higher than the cost of a community college education. If the noun in question is not a number, then "more" is correct. For example, "The cost of an uneducated society is more than the cost of an educated society." In the first example "cost" refers to a number and in the second "cost" is not countable the way tuition is.

In this situation it is far better to use more as an adverb. The first sentence leaves the listener wondering why the speaker didn't just say this:

X costs more than Y.

This one is fine, albeit verbose:

The cost of X is higher than the cost of Y.

The words "great" and "greater" are used with intangible costs (but not exclusively with such costs):

Henry's rise to the top in the sport of boxing came at a greater cost to his health than all the prizes he ever won.

"more" does not work with nouns very well, unless they are numbers. And this means they have to grammatically be numbers, and not merely look like numbers or have a semantic connection with numbers:

The number of apples on the table is { ? more | greater } than the number of oranges on the same table.

Paradoxically, the word "number" is not a number! But:

There are more apples than oranges on the table. [Different role of "more".]

Three apples is more than two apples. [Three is a number.]

Three is { more | greater } than two.

The number three is { *more | greater } than the number two.

Like the word "number", the word "cost" is not a number, even if the cost is semantically identifiable with concrete dollar figure. Semantically a cost (of this type) is some kind of number, but grammatically it isn't. Thus:

Three hundred dollars is more than two hundred dollars, but the cost of a three hundred dollar item is higher than the cost of a hundred dollar item.

It may help to look at another word instead of cost. How about "damage":

In last week's accident, the damage to the passenger car was {*more | greater} than the damage to the truck.

The car was more damaged than the truck.

According to the insurance adjustor, the damage {is | comes to | is estimated at} more than three thousand dollars.