Let's review what happens when the neutral goes open at any point in the circuit between the panel and the stove. The stoves 120 volt loads will serve as rather low resistance conductors between one of the ungrounded conductors and the frame of the stove. Another poster has alleged that that is not a problem because you will be in series with the load. When two impedances are in series the largest quantity of the voltage will be reflected across the higher impedance. In the circuit in question the higher impedance is the human being. If the voltage applied across that human being is higher than 30 volts there is a likelihood that that person may be injured or killed the only thing missing is contact with another conductive surface that happens to be grounded. The kitchen sink, refrigerator, dishwasher, and even many kitchen floor coverings are sufficiently conductive to provide that conductive pathway.
It has also been alleged that it makes no difference because both conductors terminate on the bonded buss bar of the service equipment enclosure. That position ignores the fact that since the neutral conductor carries current it expands and contracts with each use of the appliance. As a result of that normal thermal cycling it's connections are under far more stress than those of the equipment grounding (bonding) conductor.
In the older three wire configuration any failure of the neutral conductor energizes the frame to the potential of the circuit. In the four wire configuration the neutral opening causes the appliance to stop functioning but the frame will remain at zero volts relative to other grounded surfaces.
I'm only one member of the entire nations fire service and I have attended three accidents that were secondary to failure of neutral terminations on three wire appliances. It is true that I have been in active service for thity plus years. One was an electrocution. the other two were electrical injuries that were short of being fatal. One was a working code who then spent weeks in the hospital and was provided with an implanted defibrillator while her injured heart muscle healed. The other suffered a dislocated shoulder and a fractured arm as a secondary effect of the severe muscle contractions that occur during electric shock. In all three cases the appliance in question was an electric clothes dryer were the frame was bonded to the neutral.
It is your house and your family so which one do you think is better.
-- Tom H