Some discussion of why the twin behaves the way Crab and John E have so properly described:
In the vertical takeoff, the loss of an engine creates a power deficit that produces the need to descend, of course. The deficit is measured by comparing the power needed to HOGE as compared to the OEI power remaining. If the OEI power is very close to the OGE power, as is the case when very lightly loaded, the ride down is fairly slow and the landing easily cushioned. Since the speed of that descent is driven by the size of the power deficit, as the takeoff mass is made greater, the OEI power deficit is greater, and the rate of descent becomes greater. If the power deficit is appreciable, the aircraft doesn't stabilize in a fixed rate of descent, it actually accelerates downward, so that the stop at the bottom becomes pretty harsh at higher reject altitudes (higher barriers) and at higher weights. The flight manual WAT curve (Weight, Altitude, Temperature) shows the weights where the power ratio is acceptable to perform the published procedure. For vertical procedures, the WAT curve calls for much less all up mass than a ground level procedure where you can accelerate to somewhere close to VY before the engine failure. Of course, the ground level procedure rejects into a much longer heliport, because you have to bring that fast helicopter to a stop while in the protected runway length. In other words, the various procedures for Cat A swap all up mass for speed/runway length.
VRS is somewhat involved in a vertical reject, but the descent is more governed by the simple application of too little power and too much mass, so rotor thrust does not equal weight, and the helo falls, and accelerates as it falls.
Generally, for a vertical reject from over 100 feet to be successful, the OEI power must be an appreciable fraction of the OGE power required, perhaps 75 to 80%. That is almost exactly what HIGE power is as compared to HOGE, so a rule of thumb could be that if you can barely HOGE OEI, you probably have a darn good vertical reject capability.