when the engines fail, or are set to idle the aircraft has a limited store of energy. This stored energy is made up of potential energy (weight x height) and kinetic energy 1/2 mass x velocity squared. From the start of the glide the stored energy is depleted in pushing the aircraft forward against the drag force.
When the energy store is completely exhausted the aircraft will be standing still on (or in) the ground. Unless the engines are restarted, this energy cannot be replenished. So for maximum glide endurance, which means minimum rate of descent, the glide must start at the maximum possible height (giving max potential energy), then it must be flown at the speed at which energy depletion rate is least. But energy depletion rate is power required, so maximum glide endurance from any given height is achieved by flying at Vmp.
Power required is equal to drag x TAS, so with both aircraft at the same speed (as specified in the question), the heavier aircraft which will be generating more induced drag, will require more power. So the heavier aircraft will deplete its energy faster than the lighter aircraft. This means that the heavier aircraft will be descending faster than the lighter one.
As stated in my original post, the overall effect depends upon what identical speed both aircraft are flown at. High speeds will tend to favour the heavier aircraft and low speeds will tend to favour the lighter one.
Why do gliders carry water?...... Because this enables them to glide faster. For maximum glide range, you must fly at Vmd and Vmd is proportional to the square root of the weight. So if you are in a glider race and want to get to a fixed point before the competition, it is useful to increase your weight by carrying water. But if you want to glide for the longest time you must dump the water to miniimise your energy consumption rate.
Think about it..........If increasing aircraft weight will increase glide endurance then something like an A380 will almost be able to glide forever. Do we really believe this??????