The best way of observing prayer at night as taught by the Holy Prophet sas is to observe tahajjud individually at home.
The Prophet(Sahih al-Bukhari, Book 96, Hadith 21)
sastook a room made of date palm leaves mats in the mosque. Allah’s Messenger sasprayed in it for a few nights till the people gathered. Then on the fourth night the people did not hear his voice and they thought he had slept, so some of them started humming that he might come out. The Prophet sas then said, “You continued doing what I saw you doing till I was afraid that this might be enjoined on you, and if it were enjoined on you, you would not continue performing it. Therefore, O people! Perform your prayers at your homes, for the best prayer of a person is what is performed at his home except the compulsory prayer.”
During the time of Hadrat ‘Umar ra, people began finding it difficult to observe tahajjud individually at home, so he had the practice of tarawih started for such people as a replacement for tahajjud, not as a supplement to tahajjud.
I went out in the company of ‘Umar bin al-Khattab one night in Ramadan to the mosque and found the people praying in different groups. A man praying alone or a man praying with a little group behind him. So, ‘Umar said, “In my opinion I would better collect these (people) under the leadership of one reciter.” So, he made up his mind to congregate them behind Ubay bin Ka‘ab. Then on another night I went again in his company and the people were praying behind their reciter (qari). On that, ‘Umar remarked, “What an excellent bid’ah [innovation in religion] this(Sahih al-Bukhari, Book 31, Hadith 3).
is;but the prayer (tahajjud) which they do not perform, but sleep at its time is better than the one (tarawih) they are offering.” He meant the prayer in the last part of the night. (In those days) people used to pray in the early part of the night
Ordinarily, an innovation (bid’ah) is a bad thing, the Holy Prophet sas said:
The worst practice is the introduction of new practices in Islam and every innovation (bid’ah) is a misguidance.(Sahih Muslim, Book 7, Hadith 55)
However, the reason tarawih is an “excellent innovation” (ni’mal bid’ah) is that it does not add anything to tahajjud, it is a different form of tahajjud. Hadrat Khalifatul-Masih IV rta explained that it is like tayammum done to replace wudu in the absence of water (Urdu Mulaqat Session 8, March 22, 1994).
If someone observed tayammum and then he finds water, then he should observe wudu as well. If someone observed
Tarawih was started in the time of Hadrat ‘Umar so that those who cannot get up for tahajjud can have their voluntary worship done and they can listen to the Quran from a reciter (qari). But those who can get up for tahajjud, they should also read tahajjud.(Friday Sermon, July 3, 2015)
Tarawih is primarily for those who are weak in tahajjud, but that doesn’t mean they should give up on trying to get up for tahajjud altogether. Those who are weak in tahajjud should observe tarawih regularly and keep trying to get into the habit of observing tahajjud.
However, if a trend begins where we start to believe that supplementing tahajjud with tarawih is a better practice than the practice of the Holy Prophet
Qiyame Ramadan, which people call tarawih, is not any separate prayer, it is the same tahajjud that righteous Muslims observe year round… Tarawih and tahajjud are one thing. To observe both while thinking they are two separate worships is incorrect.(Fatawa Hadrat Musleh Mau‘ud, p. 171).
If someone has water, then it is not more righteous for him to observe both tayammum and wudu. Similarly, if someone wakes up regularly for tahajjud, then it is not more righteous for him to observe tarawih along with tahajjud. The most righteous practice is to observe only tahajjud individually. This was the regular practice of the Holy Prophet
If someone observes both tarawih and tahajjud, we should not try to stop him because we do not know his intention. The Promised Messiah as narrates that once someone was observing Salat at the wrong time and someone asked Hadrat Ali ra why he did not stop him. Hadrat Ali r said:
I do not wish to come under this verse.(Tafsir Hadrat Masih Mau‘ud, vol. 8, p. 417, 96:10–11)