עָלֵֽינוּ לְשַׁבֵּֽחַ לַאֲדוֹן הַכֹּל
לָתֵת גְּדֻלָּה לְיוֹצֵר בְּרֵאשִׁית...
It is our obligation to praise the Master of all, to ascribe greatness to the Creator of the [world in the] beginning...
The meforhsim say that we use the term Shevach specifically by Adon HaKol because Shevach represents continuously becoming "better" and infinite, and therefore we say that next to Adon HaKol in order to dismiss the notion that Hashem is just an Adon.
And also we say Gedula to praise the Yotzer Bereishis to dismiss the notion that Hashem created the world and then left, and we therefore say that Hashem is also "Gadol" which represents his involvement in the world.
And also we say Gedula to praise the Yotzer Bereishis to dismiss the notion that Hashem created the world and then left, and we therefore say that Hashem is also "Gadol" which represents his involvement in the world.
In Shabbos Shacharis we say:
(ב) חו”ק אֶחָד אֱלהֵינוּ. גָּדול אֲדונֵינוּ. קָדושׁ שְׁמו:
Here we say the terms that already "match", it makes sense that the Adon HaKol willl be "Gadol" and involved because He is the Master after all. So it seems that here we are saying the direct shevach of Hashem, whereas in Aleinu we are stressing the opposite praises to each attribute of Hashem to dismiss any false notions someone might think up.