Reading Quran during Ramadaan is one of the best and most virtuous of good deeds, because Ramadaan is the month of the Quran. Allah says (interpretation of the meaning):
“The month of Ramadan in which was revealed the Quran, a guidance for mankind and clear proofs for the guidance and the criterion (between right and wrong)”
Jibreel used to come to the Prophet (peace and blessings of Allah be upon him) every night in Ramadaan, and study the Quran with him. Narrated by al-Bukhaari, 5; Muslim, 4268.
Al-Bukhaari (4614) narrated from Abu Hurayrah (may Allah be pleased with him) that Jibreel used to review the Quran with the Prophet (peace and blessings of Allah be upon him) once each year, and in the year in which he died, he reviewed it with him twice. From this it may be understood that it is mustahabb to read Qur’aan a great deal and to study it during Ramadaan.
It may also be understood that it is mustahabb to complete the Quran (during Ramadaan), because Jibreel (peace be upon him) used to review the entire Quran with the Prophet (peace and blessings of Allah be upon him).
Both memorizing and reviewing are reading, because no one can memorize or review except after repeatedly reading the verse several times, and for every letter there is a reward of ten hasanahs.
Based on this, it is better to focus on memorizing and reviewing.
So the Sunnah indicates that:
1- We should review what we have learned
2- We should study together
3- We should read. This is achieved when doing the first two.
In this case a person should complete the Quran, even if it is only once during the month, then he should do whatever is most appropriate in his case, either reading more and completing the Quran, or focusing on reviewing, or memorizing new passages. He should do what is best for him. It may be better for him to memorize or read or review. The Quran is meant to be read and pondered, and it is meant to influence and be acted upon.
The believer should examine his heart, see what is best for him, and do that.
And Allah knows best.