The difference can be large -- 30 cal/molK for [PPh4]+ at pbe0/cc-pvdz -- which becomes quite significant when multiplied by T (e.g. 298.15 K).
Note that the rotational entropy term also may differ, but that this would be due to different uses of symmetry in the calculations: http://molecularmodelingbasics.blogspot.com.au/2012/12/conformational-and-rotational-entropy.html
If you turn off symmetry (noautosym) in nwchem the rotational entropy will not be corrected. I've noticed that Gaussian, on the other hand, will sneakily apply correction if it finds an acceptable symmetry even if you request nosymm, so make sure that you scan through the output carefully.
Either way, vibrational entropy is not symmetry dependent. Instead you will have to worry about the grid fine-ness when comparing outputs.
If your molecule is very small, such as benzene or tetramethylphosphonium, it seems that you don't have to worry about this. However, even fairly small molecules such as [PPh4]+ will be affected.
Conv. Dens. = Convergence Density
|Code||Symm||Grid||Conv. Dens.||DFT Energy||ZPE||HCorr||S(tot)||S(trans)||S(rot)||S(vib)|
F=fine. X=Extrafine. U=Ultrafine.
S(rot) values in blue are symmetry corrected. That's completely normal.
With "grid fine" NWChem gives a very different result to G09.
You can see the difference in the predicted IR spectra as well.
Fine (NWChem) (blue rings) vs G09 (red circles):