Papers with DFT calculations that use VASP work with PAW pseudopotentials which are also available in PS Library. I assume they are different since VASP is commercial. Given that, how different are they in terms of accuracy?
This isn't a perfect comparison of what you asked, but I think it can help. I'll refer to PAW datasets as "pseudopotentials" here since that is how they are used in practice.
According to this relatively recent paper, when compared to all-electron calculations, the Standard Solid State Pseudopotential library (which has many PSLibrary pseudopotentials in it, though it is a mix of PAW, ultrasoft and norm-conserving ONCV from a few sources) is comparable in accuracy (delta gauge 0.5) to VASP PAW (delta gauge 0.6). When comparing only PSLibrary 1.0.0 PAW (which, if you read the documentation, was "updated" simply to improve the consistency of the pseudopotential generation approach, not necessarily make individual pseudopotentials more accurate), the delta gauge was slightly higher at 0.9. If you wanted to make an "optimal" set of PAW datasets from PSLibrary, using a mix of version 1.0.0 and older pseudopotentials (choosing the best from https://materialscloud.org/) they would probably be comparable in accuracy vs. VASP, at least when using the delta gauge metric.
There are also other things to consider, such as the specific subset of PAW (high or low accuracy), and the accuracy you get vs. the "hardness", i.e. how low of an energy cutoff you can get away with. I don't think there's a thorough analysis of this, but while both commercial and non-commercial software have their pros and cons, I don't think you will necessarily have more accurate results from a commercial code.