Plasma-based positron sources are attracting significant attention from the research community, thanks to their rather unique characteristics, which include broad energy tuneability and ultra-short duration, obtainable in a compact and relatively inexpensive setup. Here, we show a detailed numerical study of the positron beam characteristics obtainable at the dedicated user target areas proposed for the EuPRAXIA facility, the first plasma-based particle accelerator to be built as a user facility for applications. It will be shown that MeV-scale positron beams with unique properties for industrial and material science applications can be produced, alongside with GeV-scale positron beams suitable for fundamental science and accelerator physics.