"Two Fewer Items" or "Two Items Fewer"?

Question

If I have 10 items in my bag and my friend has 12, which of the following do I say?

I have two fewer items than they do.

or

I have two items fewer than they do.

In this page from CMOS, they say:

There are two fewer food groups in the new pyramid.

Does the order matter?  Do different style guides encourage the use of different orders?

Note: this is not a question about "fewer" versus "less."

herisson · Accepted Answer

Either is grammatical, according to the Cambridge Grammar of the English Language (Huddleston and Pullum 2002).

The comparative determinatives more, less, fewer can occur after the head provided there is a determiner. Thus we have a post-head alternant for one more day but not for more days: compare [One day more]/*[Days more] will be needed.

(Underlining in the original replaced by brackets, p.445)
I haven't yet found a style guide that addresses usage of the two word orders.
Here is a Wordreference thread about " I ran 2 more miles than her" vs. "I ran 2 miles more than her".

Will Crawford · Answer

"Two items fewer" is ungrammatical because fewer refers to the number of items, rather than the items themselves.  Therefore, "two fewer items" is correct.
So,

two fewer items

is correct, meaning the count of my items is two lower than the count of theirs.

"Two Fewer Items" or "Two Items Fewer"?

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