One point of similarity between the language of the first proposal and the second is that in both he begins with utter frankness and also with intense emotion. For example, in his first proposal he begins with the very direct, very frank, and very emotionally tense statement, "In vain have I struggled. It will not do. My feelings will not be repressed. You must allow me to tell you how ardently I admire and love you" (Ch. 34). This is a very honest and direct statement because it is clear that he is speaking of his feelings because he can no longer keep himself from doing so.
Likewise, we see a similar beginning in the second proposal. After Elizabeth wholeheartedly thanks him for rescuing Lydia and her family, he renews their conversation about marriage by saying that he knows Elizabeth's character is too giving to say something only for the sake of teasing his feelings. He then makes the very direct and honest statement that his feelings for her have not changed and very frankly asks her to tell him if her feelings for him are still the same, as we see in the lines:
You are too generous to trifle with me. If your feelings are still what they were last April, tell me so at once. My(it) affections and wishes are unchanged, but one word from you will silence me on this subject for ever. (Ch. 58)
However, the biggest difference between the two proposals is content. In the first proposal, though Austen does not tell us his actual words, he tells her how he believes her family to be inferior to himself and that marrying her would be a "degradation" of his pride. But by the time he delivers his second proposal, he has changed his attitude a great deal. He even confesses that though he was raised to learn "good principles, [he was] left to follow them in pride and conceit" (Ch. 58). He was encouraged to be selfish and to think "meanly of all the rest of the world" except his own family.
Hence, in both proposals, Darcy's language is still just as direct, frank, and honest. The only true difference is that the words express the different beliefs he now holds.