The link depicted at the end of this answer depicts the pros and cons of different DFT calculation packages (e.g. Gaussian, VASP, CP2K, Quantum ESPRESSO, FHI-aims).
Quantum Espresso (QE):
Advantages: QE is the open source version of VASP - its main pro is that it is free. Also it is easier to develop new functionality for it and there are probably a few more extensions. If something is broken or missing, you can fix it or add it yourself.
Disadvantages: It is slightly worse than VASP in the VASP pros categories. It is also a planewave basis, so that VASP pro and con applies (see text below).
VASP Advantages & Disadvantages:
Advantages: It is widely used, actively developed, comes with a psuedopotential library, usually has cutting edge improvements (hybrid functionals, GW, etc), can be interfaced with other software, is well-parallelized, and is efficient. It is also more convergent because it uses a planewave basis.
Disadvantages: Its easy to abuse, its expensive, you are reliant (more or less) on the psuedopotentials shipped with the source, and the planewave basis and attendant periodic boundary conditions can (very rarely) cause problems. I say this rarely causes problems because the efficiency boost you get from the Fast Fourier Transform (FFT) and the good parallelization mean you almost always come out ahead compared to a code in a local basis when you are trying to simulate an isolated molecule. You do this simulation in VASP by adding regions of vacuum around your isolated system.