Roman sculpture was heavily influenced by Greek sculpture. In fact, many of the Roman sculptures were just copies of Greek sculptures. But the Roman sculpture was created to serve a purpose: namely, to impress the public - to communicate the power and majesty of Rome. Sculpture on Roman buildings could be merely decorative or have a more political purpose, for example, on triumphal arches the architectural sculpture captured in detail key military events
which reinforced the message that the emperor was a victorious and civilizing person across the known world. In this aspect the purpose of Roman sculpture was to record their history as it happened. The Ancient Romans decorated with sculptures not only public buildings and parks, but also private homes and gardens. In this sense the Roman sculpture played an important part of the Roman daily life. The wealthy Romans decorated their large homes with sculptures. A lot of times these sculptures were of themselves or their ancestors. Other popular subjects for sculptures included gods and goddesses, philosophers, famous athletes, and successful generals.
The purpose of the paintings however was mostly decorative, created to please the eye of the viewer. The walls of the homes of wealthy Romans were often decorated with paintings. These paintings were frescos painted directly on the walls. Most of these paintings have been destroyed over time, but some of them were preserved in the city of Pompeii when it was buried by the eruption of a volcano.
To conclude I think the purpose of sculpture and painting in Rome from esthetical point of view is practically similar - to decorate buildings (be it private homes, or public building) and to make them more beautiful. However there is a second layer to the purpose of the sculpture of Rome, namely to use it as political propaganda.