With the Materials Project and magnetism, it's often useful to download the structure directly and examine the magnetic moments on that structure, for example using the pymatgen Python code and the MPRester class, like so:

from pymatgen import MPRester
with MPRester() as mpr:  # you may need to supply your API key in the parentheses here, see materialsproject.org/dashboard
    struct = mpr.get_structure_by_material_id('BaVSe3')
print(struct)

For this mp-id, this gives:

Full Formula (Ba2 V2 Se6)
Reduced Formula: BaVSe3
abc   :   7.035690   7.035690   5.902194
angles:  90.000000  90.000000 119.366265
Sites (10)
  #  SP           a         b         c    magmom
---  ----  --------  --------  --------  --------
  0  Ba    0.663884  0.336116  0.754951     0.001
  1  Ba    0.336116  0.663884  0.254951     0
  2  V     0.974167  0.025833  0.013237     1.029
  3  V     0.025833  0.974167  0.513237     1.041
  4  Se    0.329967  0.163445  0.243081    -0.061
  5  Se    0.836555  0.670033  0.243081    -0.063
  6  Se    0.829283  0.170717  0.274618    -0.082
  7  Se    0.163445  0.329967  0.743081    -0.06
  8  Se    0.670033  0.836555  0.743081    -0.062
  9  Se    0.170717  0.829283  0.774618    -0.083

This is in units of Bohr magneton, so the moment on the V is 1.029 µB, and the total moment per unit cell is 1.66 µB (sum(struct.site_properties['magmom'])).

Why the discrepancy?

Two reasons,

1. in a DFT calculation, the magnetic moment you obtain is very sensitive to both your initial ordering (ferromagnetic, antiferromagnetic, etc.) and also your use of Hubbard U. It is very common that different authors use different U values. The Materials Project uses a U of 3.25 eV on vanadium. This can also be affected by pseudo potentials, which will necessarily be different between simulation code like Quantum Espresso and VASP.

2. the discrepancy on Materials Project could be the result of our slow-but-steady progress towards more explicitly calculating magnetic order of materials (e.g. see this paper). While the values reported by MP from an individual calculation always remain the same, the values reported on the "material details page" can change from release to release as new calculations come in, and bug in this case is also possible (we strive for quality but it's a large database and bugs do happen, we encourage people to check our database release logs where we disclose issues as we discover them).

We (meaning, people working on the Materials Project) try to be responsive on matsci.org/materials-project if you want to ask a question directly, or you can contact us over email.

In conclusion, your value of 1.95 µB per cell actually seems fairly reasonable!

Hope this helps!