Ultimately, the major change was that Christianity became the official religion of the empire, doing away with centuries of traditional ways. Edward Gibbon argued that Christianity also helped destroy the empire, but his view is no longer accepted by most scholars.
Gibbon argued that Christianity made Romans less vigorous. He argued that it made them focus on the next life and therefore neglect things like the defense of Rome.
Historians can agree today that the adoption of Christianity under Constantine changed Roman society. It led to Constantine abolishing the pagan temples and appropriating their wealth. It led to the abolition of the gladiatorial games. It (arguably) led to other such laws, such as a ban on infanticide, that were more humane from the modern point of view than Roman laws were before. In these ways, Christianity can be said to have made Rome less brutal in addition to simply changing Roman society by doing away with the connection between the government and the old pagan religion.
Although the Emperor Constantine issued the Edict of Milan in 313, legalizing Christianity, it can be difficult to parse out a direct influence of the faith on the Roman Empire, as Christianity was only one of a number of competing pressures brought to bear on the empire during this time of dissolution. However, many historians agree on two impacts: the ascension of monotheism and a greater, if not great, social equality.
While the extent of Constantine's Christian conversion has been debated, he undoubtedly tolerated and even embraced Christianity while also holding to a pagan worldview based on religious pluralism: he was perfectly comfortable, say, with going from overseeing the Council of Nicea, which was pounding out the details of Christian doctrine, to sacrificing a bull to the god Jupiter in Rome. In fact, archeological evidence shows that many Christians in Rome after legalization were buried with both Christian and pagan artifacts, indicating that they too were comfortable with the idea of religious pluralism. However, that changed in the 380s when the Emperor Theodosius officially outlawed other religions. This may have reflected social changes already in place (a falling off of pagan religious following) but it helped cement the idea of one God and one state religion that, for better or worse, trailed Europe into the Middle Ages.
The Roman writer Celsus scorned the growing Christian movement as comprised of women, children and slaves, all second class entities in the Roman state with almost no rights beyond being the property of higher status males in a patriarchal social order. New Testament evidence supports Celsus's view that women and slaves had a significant representation in early Christianity. It is no mystery why a religion that purported to see no male or female, slave or free, in the eyes of its God might win the support of subaltern groups. Early Christians also apparently took seriously the command "feed my sheep" and engaged in charitable works among the poor and the sick that gained converts. While Rome would never become anything close to a model of egalitarian principles, Christianity did disseminate ideas of human equality, and evidence indicates that groups such as women enjoyed higher status within the church than in the society as a whole.