In a novel where the spoken word rules the day, and where private thoughts don't have too much presence on the page, letters are a stand-in for the interior lives of the characters. Look at Mr. Collins's first letter:
As a clergyman, moreover, I feel it my duty to promote and establish the blessing of peace in all families within the reach of my influence; and on these grounds I flatter myself that my present overtures are highly commendable, and that the circumstance of my being next in the entail of Longbourn estate will be kindly overlooked on your side, and not lead you to reject the offered olive-branch. I cannot be otherwise than concerned at being the means of injuring your amiable daughters, and beg leave to apologise for it, as well as to assure you of my readiness to make them every possible amends—but of this hereafter. (13.16)
And then compare it to Mr. Darcy's letter to Lizzy:
Be not alarmed, madam, on receiving this letter, by the apprehension of its containing any repetition of those sentiments or renewal of those offers which were last night so disgusting to you. I write without any intention of paining you, or humbling myself, by dwelling on wishes which, for the happiness of both, cannot be too soon forgotten; and the effort which the formation and the perusal of this letter must occasion, should have been spared, had not my character required it to be written and read. You must, therefore, pardon the freedom with which I demand your attention; your feelings, I know, will bestow it unwillingly, but I demand it of your justice. (35.4)
Mr. Collins is all "me, me, me," just like he is in real life. But Mr. Darcy's letter is different. Sure, he talks about himself—but only in relationship to Lizzy. His letter is all about making connections and trying to communicate. Lizzy doesn't exactly fall in love with him after this letter, but it doesn't take much longer.