Will he who did not enjoy a good life in this world be compensated in Paradise, if he and another person are equal in piety and righteousness and both enter Paradise, or will they receive the same reward, such that the former would have gained both this world and the Hereafter, and would this be considered unjust to the latter?

The basis for distinction in the Afterlife is piety (taqwa (definition)) and righteous deeds. The poor will enter Paradise before the rich due to the lightness of their accountability. Scholars have debated which is better: the grateful rich person or the patient poor person. The correct view is that superiority is determined by faith and piety. Allah Almighty chooses and bestows His favor upon whomever He wills with prophethood, dominion, and health. This is not injustice, for Allah knows best where to place His message, and it is He who distributes livelihoods among His servants, and "That is the Bounty of Allah; He grants it to whom He wills." A servant has no right to object to his Creator or accuse Him of injustice.