What is the difference between agree and concur? Which is the more common to use? For instance, someone said something to me and I want to say that he is right. Should I say I agree with you or I concur with you?
As @Jasper says, the words mean pretty much the same thing. I suppose concur could be a little bit more "formal" than agree, in that it's not so well-known. But that's really just because it's "dated". From Google Ngrams:
In answer to OP's specific question, use agree unless you want to sound stilted / pretentious. Whilst there's no grammatical reason why with you is any more "correct" after either verb, in terms of usage I suspect it may be omitted more often after concur. I suggest that purely because the brevity of I [verb] can carry "imperious" overtones, better suited to the more formal concur.
Reflecting on this, I think that concur describes a passive acquiescence, agree an active one. Imagine a meeting. The Chair says Are we in favour of what is proposed? This is followed by heads nodding wisely and a general murmuring suggesting that those present approve, that is, they 'go along with it', they concur.
Now imagine a different meeting. The Chair again says Are we in favour of what is proposed? One of those round the table says This is a bold initiative and we should give it our support.’ Another says I did have some reservations, but I can now see the advantages and you can rely on my vote. And so on. Individually and collectively, they agree.
Concurring, I think, has the connotation that you are coming to agreement with a group consensus that is in the process of forming. In other words, the group is coalescing around a particular position, and you are helping that coalescence. Agreement is usually more directed towards a statement that someone else just made.
My understanding is that concur has a connotation that the speaker had already formed an opinion (before hearing the opinion of the other party), and that those two opinions are in agreement.
On the other hand, agree does not carry any such connotation. In other words, the speaker may or may not have had an opinion before hearing the one that they are agreeing with.
To concur is to express agreement.
Although there's significant overlap and it's almost never wrong to use one instead of the other, there is a subtle difference. If you concur with someone, you express the same view they do. Agreeing can be just a state are in, one of holding the same view as someone else. Concurring is an act you perform, the act of expressing agreement with another's view.
While "agree" is certainly sometimes used to express the act of agreeing, "concur" is almost never used to express the state of agreement. For example, if a board of directors gets together and all of them think closing the company is best but they haven't discussed it yet, you could say: "Though they hadn't discussed it, they all agreed that closing the company would be best." But you would not say: "Though they hadn't yet discussed it, they concurred that the best option was to close the company." You can say "they would soon concur".