Is it true that converts to Islam receive a greater reward and recompense than Muslims born into it, by analogy with the incident of Khalid ibn al-Walid and the Roman commander Gorge?

There is no necessary correlation between a person's inherent virtue and their religion, and whether they were born Muslim or embraced Islam later. The essence of virtue lies in piety (taqwa (definition)), as Allah Almighty says: (Indeed, the most noble of you in the sight of Allah is the most righteous of you). And it may be that one who embraced Islam after disbelief is superior to one who was born into Islam, if they are more pious towards Allah, because what truly matters is the ultimate outcome. The Companions who believed after their disbelief are superior to their children who were born into Islam.

As for the account of Jurja the Roman embracing Islam at the hands of Khalid ibn al-Walid, its chain of narration is very weak and cannot be used as evidence. Its chain includes Sayf ibn Umar, who is abandoned and accused of heresy, and Shu'ayb, who is unknown, and the biography of Abu Uthman Yazid ibn Asid is not known.