The appeal of I-84 is three-fold: (1) lower tolls, (2) less congestion east of the Hudson up through New England, and (3) better connections to the interior of North America outside of congested urban centers.
I agree all these things are true of I-84, which crosses the Hudson on the Newburgh - Beacon (Hamilton Fish) Bridge. I sort of gather that you understand this from the comments, but for those who aren't familiar with the geography here, it is I-87 (New York Thruway) that crosses on the Tappan Zee Bridge about 30 miles downriver from Newburgh and I-84.. And the Tappan Zee is about 25 miles upstream from the GW on which I-95 crosses.
On the points mentioned however(tolls and congestion), both Newburgh - Beacon and Tappan Zee hold the advantage over the GWB.
For what it's worth, if I have occasion to cross the Hudson for any destination south of The Bronx you will find me driving through scenic New Jersey to Secaucus and taking the train to Penn Station to avoid all the unpleasantness of highway crossings and the impossible parking rates in the former fiefdom of once-imperial-highness bloooomburg(h).. ;-)