What is the significance of this? It is because the nights represent difficult times, and in those times, Hashem cares for us like a father cares for his children. The mornings represent happier times, when Hashem's chesed is clearly felt, as it states (Tehillim 92:3) ָחַס ְדֶּך בַּבֹּקֶר לְה ַגִּיד, "To tell in the morning Your kindness." At those times, Hashem is close to us, like a king who is close to his people, but not on the intimate level of a father and child.
We find this difference in the brachos that we say after kriyas Shema in the morning and in the evening. In the morning, the Jewish nation is referred to as ידידים, keviyachol, friends of Hashem. As we say, וידידים זמירות ידידים ונתנו ...העברת, "The friends you let pass.... The friends offered music, songs, and praises." In the evenings, we are called בנים, as we say in this brachah, גבורתו בניו וראו ...סוף ים גזרי בין בניו המעביר, He carried his children between the split Yam Suf.... His children saw His strength."
A ידיד is a good friend, you greet him with a happy countenance when you say Gut Shabbos or when you greet him I the morning, but it doesn't compare to the love one has for his own children. The brachah at night, which represents more challenging times, discusses the higher form of love, because when people go through hard times, that is when they merit Hashem's utmost love.
Also, Klal Yisrael are called בנים, children, twice in the Torah. Once is (Shemos 4:22) בְכֹרִי בְּנִי 'ה אָמַר כֹּה פ ַּרְעֹה אֶל ָּוְאָמ ַרְת יִשְׂרָאֵל, "You shall say to Pharaoh, 'So said Hashem, "My firstborn son is Yisrael." Another time is (Devarim 14:1) לָמֵת עֵינֵיכֶם בֵּין ק ָרְחָה תָשִׂימוּ וְלֹא תִת ְ גֹּדְ דוּ לֹא א ֱלֹק ֵיכֶם 'לַה אַת ֶּם בָּנִים, You are children of Hashem, your G-d. You shall neither cut yourselves nor make any baldness between your eyes for the dead." This is because both pasukim speak about the Jewish nation when they are at a low level. The first pasuk discusses the time the Yidden were suffering in Mitzrayim. The second pasuk refers to a person experiencing the loss of a relative, r'l. Specifically at these hard times, Hashem calls us בנים, children. These are the times that Hashem's love for us is at its peak.
