Although reading or reciting the Qurʾān is always rewarding, doing so during the blessed month of Ramaḍān is much more rewarding since the Qurʾān was revealed in Ramaḍān. Allāh said:

شَهْرُ رَمَضَانَ الَّذِي أُنزِلَ فِيهِ الْقُرْآنُ ‎﴿١٨٥﴾

“The Qurʾān was revealed in the month of Ramaḍān.”
[Al-Baqarah, 2:185]

Additionally, Jibrīl would review the Qurʾān with the Messenger (ﷺ) during Ramaḍān. ʿĀʾishah (رضي الله عنها) narrated: “Jibrīl would meet Allāh’s Messenger (ﷺ) during the entire month of Ramaḍān to review the Qurʾān.” (Reported by Muslim with this wording)

Therefore, reading or reciting the Qurʾān in Ramaḍān is much more rewarding. However, doing so during its nights is better than doing so during its days, since Jibrīl would review the Qurʾān with the Prophet (ﷺ) during the nights of Ramaḍān.

Ibn ʿAbbās (رضي الله عنه) said: “The Prophet (ﷺ) was the most generous person, and he (ﷺ) became even more generous in Ramaḍān when Jibrīl would meet him (ﷺ). Jibrīl would meet him every night during Ramaḍān to review the Qurʾān. Allah’s Messenger (ﷺ) was more generous than a swift wind.” (Reported by al-Bukhārī and Muslim)

Therefore, Allāh himself chose Ramaḍān’s nights to send Jibrīl to review the Qurʾān with the Prophet (ﷺ) as the angels themselves only follow Allāh’s commands. They said:

‏ وَمَا نَتَنَزَّلُ إِلَّا بِأَمْرِ رَبِّكَ ‎﴿٦٤﴾‏

“We [i.e. angels] only descend when your [i.e. the Prophet’s (ﷺ)] Lord commands us to do so.”
[Maryam, 19:64]

Jibrīl would review the Qurʾān with the Messenger (ﷺ) during the night, as was mentioned in the Ḥadīth of Ibn ʿAbbās (رضي الله عنه), and this proves that reciting the Qurʾān more during the nights of Ramaḍān is recommended.

 
Furthermore, reading or reciting the Qurʾān during the nights of Ramaḍān is better because the nights of Ramaḍān are much more virtuous than its days, since Allāh chose to reveal the Qurʾān during the night. He said:

إِنَّا أَنزَلْنَاهُ فِي لَيْلَةِ الْقَدْرِ ‎﴿١﴾

“Certainly, We revealed the Qurʾān on the night of al-Qadr.”
[Al-Qadr, 97:1]

The Ḥadīth of Ibn ʿAbbās (رضي الله عنه) also proves that the nights of Ramaḍān are more virtuous than its days as Allāh himself chose Ramaḍān’s nights to send Jibrīl to review the Qurʾān with the Prophet (ﷺ).

Ibn Ḥajr (رحمه الله) stated: “The Ḥadīth of Ibn ʿAbbās (رضي الله عنه) proves that the nights of Ramaḍān are more virtuous than its days.” (Fatḥ al-Bārī, vol. 9, pg. 45)

Finally, reading or reciting the Qurʾān during the night, especially after having some sleep, is better because the worshipper is usually much more tranquil and focused at this time, since he is free to reflect on Allāh’s words and ponder its meaning. Allāh said:

إِنَّ نَاشِئَةَ اللَّيْلِ هِيَ أَشَدُّ وَطْئًا وَأَقْوَمُ قِيلًا ‎﴿٦﴾

“Indeed, the vigil of the night is more effective for the worshipper and better suited for recitation.”
[Al-Muzzammil, 73:6]

Ibn Rajab (رحمه الله) mentioned: “Jibrīl would review the Qurʾān with the Messenger (ﷺ) during the night, as was mentioned in the Ḥadīth of Ibn ʿAbbās (رضي الله عنه), and this proves that reciting the Qurʾān more during the nights of Ramaḍān is recommended as a person is free from his responsibilities, able to concentrate better, and able to ponder the Qurʾān more.” (Latāif al-Maʿārif, pg. 169)

Ibn Ḥajr (رحمه الله) added: “The Ḥadīth of Ibn ‘Abbās (رضي الله عنه) proves that the nights of Ramaḍān are more virtuous than its days and that the point of reciting the Qurʾān is to understand its meaning, since this is usually achieved at night, as the daily responsibilities are numerous.” (Fatḥ al-Bārī, vol. 9, pg. 45)

Therefore, not only is reading or reciting the Qurʾān during the nights of Ramaḍān much more rewarding, but the night is also much more conducive to understand Allāh’s speech, and perhaps this is why Jibrīl was sent during the nights of Ramaḍān to review the Qurʾān with the Prophet (ﷺ). And Allāh knows best.