The first words spoken on the Moon are known by heart: "That's one small step for [a] man, one giant leap for mankind."
In the sci-fi television series For All Mankind, the Soviet Union is the first to achieve a manned lunar landing, with their cosmonaut making a more boastful statement: "I take this step for my country, for my people, and for the Marxist-Leninist way of life. Knowing that today is but one small step on a journey that someday will take us all to the stars."
What else could have been uttered on radio/television by astronauts from other countries somehow winning the Moon race? Relatively liberal countries would be inclined not to rub it in too much, while authoritarian states would send their explorers off with prepared statements extolling their political systems.
United Kingdom - "A quarter-million miles we've come, and another quarter-million we'll go for Her Majesty."
France - "An unparalleled achievement today, but a mere toddle in light of what the youth will achieve after us."
German Reich - "I stand here to ensure that Aryan children will forever see in the sky no barrier to their potential."
Japan - "We have sailed through the black abyss to wish ten thousand years of life to His Majesty. Banzai!"
Red China - "See now that when the workers and peasants desire Heaven, they shall have it!"
A joint mission by several Islamic states wouldn't dare to say something that hasn't been said in the Quran, or the Shahada itself - "In the Name of Allah, the Most Compassionate, the Most Merciful" or "Verily we have honored the Children of Adam."