What happens with data in Ephemeral storage when I stop EBS backed instances?
When you stop an instance, data on Ephemeral storage is deleted. Data on EBS volumes are preserved as they exist independent of the host.
Ephemeral storage is a hard drive attached to the host machine. Since your instance does not maintain affinity with the host when stopped, you wont retain that data.
EBS volumes are like network attached storage. They exist in a storage array outside of the host and will always exist unless the volume fails (which is pretty rare)