The similarities of the two stories, "Bedtime story" and ," There will come soft rains", are the time period, unrealistic rulers, the death of a species, and the chronological similarities.
Both stories are futuristic and are ruled by beings other than humans. In "Bedtime Story", the world has been destroyed by humans, they have killed almost all mammals and have destroyed the world, making it unsuitable for them to live in. Ants take over the world and inadvertently kill the last man as he hunts a monkey. In "There will come soft rains", the world has been abandoned and all the houses except one have been burned to the ground. There are no humans and electronic and human sensitive houses rule the world.
A species of some sort is killed off in each of the stories. The ants unknowingly kill the last man in the world in "Bedtime story" after man had already destroyed the world and killed off many mammals. In "Soft Rains" the house lets a dog wither away inside of it and the last house standing is burned to the ground.
The stories could be one story if read concurrently. In "Bedtime story", the ant mentions "wars that extinguished the cities". That could be the fire that burns the house down in "Soft rains". The dog in "Soft rains" represents the species that man killed in "Bedtimes story". As the dog suffers and dies, the house does nothing and as man kills off all of a species he does nothing to preserve them. The last mans bones were turned into dust as were the ashes and smoke of the burned house, blowing away, like the Dodo's.
There are many similarities of the two stories but there are also a few differences. One wall still remains after the fire in "Soft rains", it continues to speak to the people that are not there and it behaves like nothing has happened. The house also does not seem to want to accept the absence of the humans. Given no response, the house still behaves as though people lived there.