According to the dictionary, the primary meaning of "concur" is to "express agreement" or to "approve."
Thus, if you want be super fussy, "concur" may not be a perfect synonym for "agree" because one can "agree tacitly." Of course, if you express agreement as you did, you are concurring by definition. So, yes, the two alternatives would have had identical meanings in the situation described. BUT,
and now I am moving into opinion, my experience with usage is that "concur" seems to have connotations of formal and public agreement on an important matter.
I'm tired. Pizza for dinner?
To my ear, substitute "concur" for "agree" in that exchange, and it sounds off.
To support what is a personal impression, here is a link to Ngram
Clearly, published writers find "agree" appropriate to almost 10 times the number of contexts than those where they find "concur" appropriate. I'd prefer the actual practice of writers who found publishers over the advice of any software app.