For the sake of this answer, I will translate انزل as "to send." The word "الي" means "to," and it implies something reaching something else. The word "علي" means "upon," and it implies something coming down from above.
So, the two were used in different places to accomplish both meanings. Revelations both came down from above and it reached the prophets (i.e. it was sent to and sent upon.)
It is not uncommon in the Quran for Allah to say things in different ways meaning slightly different each time. This is in order to cover different aspects of the subject.
The first verse which uses اِلَيْ goes word by word:
...قُولُٓوا اٰمَنَّا بِاللّٰهِ وَمَٓا اُنْزِلَ اِلَيْنَا وَمَٓا اُنْزِلَ اِلٰٓى اِبْرٰه۪يمَ
Say (plural, to all listeners), "We believe in Allah, and what was sent to us, and what was sent to Ibrahim...
It should be noted that اِلَيْ is also used for what was sent to Ibrahim (AS). Hence, the slight emphasis in meaning is on the fact that revelation was given to the prophets.
The second verse word by word which uses عَلَيْ is:
...قُلْ اٰمَنَّا بِاللّٰهِ وَمَٓا اُنْزِلَ عَلَيْنَا وَمَٓا اُنْزِلَ عَلٰٓى اِبْرٰه۪يمَ
Say (singular, to the Prophet), "We believe in Allah, and what was sent upon us, and what was sent upon Ibrahim...
It should be noted that عَلَيْ is also used for what was sent to Ibrahim (AS). Hence, the slight emphasis in meaning is on the fact that revelation came from above.
(This is the explanation given by Imam al-Zamakhshari in al-Kashhaaf about the usage of the two.)
Another theory that can be proposed is that عَلَيْ is used when speaking directly to the Prophet (SAW) and اِلَيْ is used when speaking to Muslims as a whole. This can be argued based on Allah using a plural "say"-command in the first verse and a singular "say"-command in the second.
There are, however, critical problems with this theory, and it is not considered correct by Tafasir I read (including al-Kashhaaf and probably the other Tafasir derived it from there as well). These are the problems:
The word اِلَيْ is also used when speaking directly to the Prophet (SAW) in many places in the Quran (e.g. 2:4, 4:105). "Surely, We have sent down to you (O Muhammad SAW) the Book [...]" (4:105)
The word عَلَيْ is used when not speaking directly to the Prophet (SAW) (e.g. 3:72, 9:64). "[...] believe in what has been sent upon these believers [the Muslims] [...]" (3:72)
It does not explain the wording change for Ibrahim (AS) and the rest of the prophets. In the first, it was "what was sent to Ibrahim," and in the second, it was "what was sent upon Ibrahim."