All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Reciting Tahlil((Lāilāhaillallāh, waḥdahulāsharīkalahu, lahul-mulkuwalahul-ḥamdu, yuḥyīwayumītu, wahuwa `alākullishay’inqadīr) 10 times after Maghriband Fajrprayers is reportedin the following Hadith:Abu Dharr narrated that The Messenger of Allah (PBUH) said: “Whoever says at the end of every Fajr prayer, while his feet are still folded, before speaking: ‘None has the right to be worshipped but Allah, Alone without partner, to Him belongs all that exists, and to Him is the praise, He gives life and causes death, and He is powerful over all things, (Lāilāhaillallāh, waḥdahulāsharīkalahu, lahul-mulkuwalahul-ḥamdu, yuḥyīwayumītu, wahuwa `alākullishay’inqadīr)’ ten times, then ten good deeds shall be written for him, ten evil deeds shall be wiped away from him, ten degrees shall be raised up for him, and he shall be in security all that day from every disliked thing, and he shall be in protection from Shaitan, and no sin will meet him or destroy him that day, except for associating partners with Allah."
Moreover, reciting remembrances of Allah in secrecy after each prayer is an act of Sunnah save for the Imam. It is recommended that he recites them in public while teaching people who follow him in prayer. But, once they learn these remembrances and become familiar with them, they should recite them in secrecy as practiced in the Prophetic Sunnah.
Furthermore, it is stated in the Shafie book [Sharih Al-Moqadema Al-Hadramiah Pg./245 ] " The recitation of supplication and remembrance of Allah should be performed in secrecy by every praying person save the Imam while teaching people, but when he's done teaching then he should return to do so in secrecy."
In conclusion, reciting remembrances by heart is more important than reciting them orallysince the former allows one to ponder upon their exact meaning and to be in complete submission to Almighty Allah. And Allah the Almighty knows best.