(In Nashville, where Vanderbilt University (same Vanderbilts) is, there must be many fried chicken joints, as is true everywhere. Do any of them offer a Vanderbilt Tender Special?)
But, anyway - the NYC never used any Vanderbilt tenders (experimentation aside, and I have never heard of any - but I wasn't there).
This is ironic as the tender was indeed designed by a member of the same Vanderbilt (Dutch: Van Der Bilt) family that created the modern New York Central. Most Vanderbilts considered the RR a cash cow and were not railroaders as such. One of their descendants was Gloria Vanderbilt.
Oil/coal have nothing to do with it. The Vandy tender will hold less water per foot of length than a box tender, of course - the water tank is a cylinder, so less volume. But - it has an advantage in rigidity, integrity and it prevents the side to side sloshing of the water, so fewer baffles are required inside the tank as compared to a box tender. Extreme sloshing causes instability and can lead to a derailment.
There also were far fewer steamer using the Vanderbilt tender design than the box tender type, so any accurate modeling will always mean fewer Vandy models.