What is the grammatical name for the phrasing of the following famous quotes?
"never was so much owed by so many to so few"
"ask not what your country can do for you, but what you can do for your country"

I don't know whether this is what you're looking for, but... 

"Never was so much owed by so many to so few" is an example of a
rhetorical device called a "tricolon."

http://humanities.byu.edu/rhetoric/Figures/T/tricolon.htm

"Ask not what your country can do for you, but what you can do for
your country" is an example of a rhetorical device called "chiasmus."

http://www.nt.armstrong.edu/term2.htm#chiasmus

"Never was so much etc" also seems to fall within the rhetorical
device of "climax", which appears on the second of the web-pages cited
by pinkfreud.

Why do you think there is one name for the phrasing and it is the same
for both sentences?  A variety of grammatical terms could be applied
to various features of both sentences.

efn is right, there is really not much similarity between the two
sentences with respect to construction or rhetorical elements.  Could
the questioner be referring to the way the negative is used?

Archae0pteryx