In any prayer you do read/recite in the two 1st raka'a al-fatiha and at least some Quran verses (or a surah). In the 3rd andd 4th raka'a you only have to recite/read al-fatiha this is for sure (this means there is a consensus about this) for the imam and a person praying alone!
Now if you are in a jama'a (congregation) then we have an Imam who is reciting for us in maghrib and ish'a and sobh=fard of fajr loudly or at least with a audible voice=jahr in the two 1st raka'at. Here we find different ahadith (hadiths) with different and contradictory information's: one saying that the recitation of the imam is sufficient, one saying a prayer without reading al-fatiha is invalid, one saying that it's not permissible to recite along with the Imam!
Abu Hurairah narrated: "Allah's Messenger turned (after praying) from
a Salat in which he recited aloud and said:
'Has any one of you recite along with me just now?'
A man said: 'Yes, O Messenger of Allah.'
He said: 'Indeed I said to myself: Why was I being contended with
for the Quran?'"
He (Az-Zuhri one of the narrators) said: "So when they heard that from
Allah's Messenger, the people stopped reciting with Allah's Messenger
in the prayers that Allah's Messenger recited aloud."
[Version from Jami' at-Tirmidhi qualified as "Hassan" with a long commentary on the rules of some madhabs and on the different sahaba who narrated the same hadith as versions of other sahaba can be found in other hadith collections. The narration on the authority of abu Huraira can also be
found in Muwata' Malik]
At-Tirmidi here made a wide discussion about the matter which i'll try to add briefly later!
It was narrated from Ata' bin Yasar that: He asked Zaid bin Thabit
about reciting with the Imam.
He said: "There is no recitation with the Imam in anything."
And he claimed that he had recited: "By the star when it goes down (or
vanishes)" to the Messenger of Allah (ﷺ) and he did not prostrate.
[Sahih Muslim and Sunan an-Nasa'i]
For the al-fatiha matter abu Huraira (May Allah be pleased with him) gave as a hint: he said read/recite it to yourself!
Yahya related to me from Malik from al-Ala ibn Abd ar-Rahman ibn
Ya'qub that he heard Abu's-Sa'ib, the mawla of Hisham ibn Zuhra, say
he had heard Abu Hurayra say, "I heard the Messenger of Allah, may
Allah bless him and grant him peace, say, 'Whoever prays a prayer
without reciting the umm al-Qur'an in it, his prayer is aborted, it is
aborted, it is aborted, incomplete.'
So I said, 'Abu Hurayra,
sometimes I am behind the imam.
'Hepulled my forearm and said, 'Recite
it to yourself, O Persian, for I heard the Messenger of Allah, may
Allah bless him and grant him peace, say that Allah the Blessed, the
"I have divided the prayer into two halves between me
and my slave. One half of it is for Me and one half of it is for My
slave, and My slave has what he asks." ' The Messenger of Allah, may
Allah bless him and grant him peace, said, "Recite." The slave says,
'Praise be to Allah, the Lord of the Worlds.' Allah the Blessed, the
Exalted, says, 'My slave has praised Me.' The slave says, 'The
Merciful, the Compassionate.' Allah says, 'My slave has spoken well of
Me.' The slave says, 'Master of the Day of the Deen.' Allah says, 'My
slave has glorified Me.' The slave says, 'You alone we worship and You
alone we ask for help.'Allah says,'This ayat is between Me and My slave,
and for My slave is what he asks. 'The slave says, 'Guide us in the
straight Path, the Path of those whom You have blessed, not of those
with whom You are angry, nor those who are in error. ' Allah says,
'These are for My slaves, and for my slave is what he asks . ' " ' "
[From Muwata' Malik, to be found also in Sahih Muslim, Sunan abi Dawod,
ibn Majah and an Nasa'i and Jami' at-Tirmidi]
- This ended up with some madhabs not to read behind the imam at all! Following the practice of the sahabi Abudallah ibn O'mar (may Allah be pleased with both of them) this is the choice of Hanafi Madhab
Yahya related to me from Malik from Nafi that Abdullah ibn Umar, when
asked if anyone should recite behind an imam, said,
"When you pray behind an imam then the recitation of the imam is
enough for you and when you pray on your own you must recite."
Nafi added, "Abdullah ibn 'Umar used not to recite behind the imam."
- Not to read behind the Imam in jahr parts of salat: This is the choice of Maliki Madhab.
- to read at least al-fatiha to yourself in the jahr parts: some while the imam reads and some after the imam finishes al-fatiha (and this would mean you won't listen to the surah the imam recites! This seems to me wrong)
Knowing this differences my personal preference is if I'm behind an imam to try to listen and follow his recitation for surah al-fatiha by moving my lips (to myself) and listen to him when reciting a surah. And in the Parts where the imam recites to himself I recite to myself and try to end the verse (or al-fatiha) which I recite when he say's "Allahu akbar" to do ruku'.
And Allah knows best