As @tchrist notes in a comment, concur and agree are "not of the same register."
Wikipedia defines register as follows:
In linguistics, a register is a variety of a language used for a
particular purpose or in a particular social setting.
Although linguists concur that registers are an important aspect of language, they do not entirely agree on their definitions of different registers. Registers are considered to express degree of formality.
A Google NGram search for "concur with" and "agree with" shows that the latter is far more common (perhaps 60 to 100 times more common); "concur" is almost nonexistent in English fiction.
The types of books in which "concur" occurs are Congressional and Parliamentary debates, formal histories and academic studies, and legal documents. For example:
The speech of James Stephen, Esq., in the debate in the House of Commons, 1809
I cannot concur with him, however, in his present proposition; I
cannot consent that we should conciliate America at the expense of
rescinding our Orders in Council on the terms proposed by her . . .
Here's an example of the two terms in one document or study of U.S. telecommunications:
Telecommunications: Agencies are Generally Following Sound ...
https://books.google.com/books?isbn=1437909043 Linda D. Koontz - 2009
Homeland Security agreed with two and disagreed with five of the seven
recommendations directed toward the department, and it did not concur
with one finding. The department agreed with our recommendations that
it establish goals and ..
The term "partially concurs" also occurs in this formal register.
My general impression is that "concur" is viewed as a little softer than "agree"--an acceptance of a position rather than all-out positive agreement.
Wikipedia: Register (sociolinguistics)