That is completely False.
I have shells that will cause a 3 to 4 inch cavitation hole when they hit something causing a large amount of damage and blood loss that will kill with any hit in the chest area.
With a bow, even if you hit the heart it will still take time, especially if you miss and then it is bleeding, suffering, and you have to track it.
At top skill in both I would say it is a tie in that both have the potential to kill instantly, a bow is more likely to harm than kill at lower skill levels though.