Vayikra. Nochach and Nistar, Second and Third Person by Korbanos. Ich und Du

The instructions of Korbanos are in third person- he. See 1:3, 1:14, 1:10, 3:1 - יקריב אתו, והקריב מן התרים,  זכר תמים יקריבנו, אם־זכר אם נקבה תמים יקריבנו . 

However, the Korban Mincha is stated in second person- you. See 2:11, 2:12, and 2:13 - אשר תקריבו, קרבן ראשית תקריבו , וכל קרבן מנחתך במלח תמלח. 

In Shmoneh Esrei, all brachos follow the format of Nochach/Nistar, with one exception. Modim could follow the same format and end with Hatov Shemo, veLo na'eh lehodos. But it doesn't. It is stated in second person - hatov shimcha, lecha na'eh lehodos.

Reb Yaakov Emden in Beis Yaakov says that the eighteen verses in Yehi chevod correspond to the brachos in Shmoneh Esrei. It has been pointed out that all but one are lashon nistar - the fourth verse, Hashem Shimcha leolam va'ed Hashem Zichrecha ledor vador. It seems that this verse corresponds with Modim. 

Why? What is the common denominator?

Rav Bergman (Shaarei Orah/Maamarim/Vayikra) points out that whereas other korbanos yield a benefit to the baalim, this is not true by a minchas nedava. No kapara at all (he quotes the Steipler in Zevachim as stating this) and the baalim never ever eats any of it. Even a Kohen doesn't eat from his own Mincha, because it's kallil. (This is an oddity that I never saw an explanation for until now!) Indeed, when discussing the Minchas Chotei, the Torah does not use the lashon nochach. 

Lechoira, you can ask that one of the Menachos mentioned above is the Minchas Ha'Omer, that is mattir Chodosh, which is a tremendous benefit. But, remarkably enough, the Sifra says that the Torah introduces the parsha of Minchas Haomer with Im to teach you that you should be makriv as a nedava, not for the toeles of hetter - ואם תקריב מנחת בכורים!

ספרא, ויקרא דבורא דנדבה, פרשה יג ב-ג

[ב] ר' שמעון אומר "ואם תקריב מנחת בכורים לשם" – זו מנחה באה חובה. יכול נדבה? כשהוא אומר (ויקרא כג, י) "והבאתם את עמר ראשית קצירכם אל הכהן" למד שאינה באה אלא חובה.

[ג] ואם כן למה נאמר "ואם"? לומר אם אתם מביאים אותה לרצון מעלה אני עליכם כאילו נדבה הבאתם אותה, ואם אין אתם מביאים אותה לרצון מעלה אני עליכם כאילו לא הבאתם אותה אלא לצורך עצמכם.

Pretty cool, no?

Rav Bergman has a different mehalach, but I would suggest that the common denominator is that both by Modim and by Korban Mincha, you are not there to get anything. By Modim, you're not saying "Give," you're saying "thank you for what you've given." Sure, there are plenty of unctuous sycophants who only express gratitude to ingratiate themselves, but that is not the intent of the bracha of Modim.

The idea is that in both cases, one is approaching the Ribono shel Olam with absolutely no self interest, only to express respect and love and gratitude. Such a person is a ben bayis, not an outsider, and the relationship is Ich/Du, Lashon Nochach.