That thread linked by @gcusello is relatively old but quite valid.
Generally speaking - in terms of the basic user's experience, they are prety similar and you could have difficult time telling one from the other.
The difference is who is responsible for the infrastructure and who does the "low-level" stuff on the environment (and what you can do there). Because obviously you don't have direct access to the underlying servers in Splunk Cloud. Some of the settings you normally can adjust from the CLI you can only manipulate via apps uploaded to the Cloud (and remember that your private apps go through the vetting process so you can't just throw anything in them). Some settings may only be set by support. Some cannot be changed. But you don't need to worry about mundane stuff like backups.
If you set up your Splunk environment in AWS (I assume that's what you mean by AWS Splunk), it's exactly like an on-prem Splunk Enterprise installation but without having to maintain the hardware.
