Umbraco Cloud and a site you host yourself can both run a serious platform. The better choice is the one your team can operate after the project team has stepped back.
What Cloud is taking off your list.
Umbraco Cloud provides the hosting, the baseline upgrades and a deployment path between environments. That is useful when you want Umbraco to carry the platform work and you want your own people focused on content and features.
It is a weaker fit when the site must live in a specific data centre, sit on a private network, or follow a hosting standard your organisation already enforces. Those constraints are not a failure of Cloud. They are a reason to say so at the start.
What you still own on your own servers.
Self-hosting means someone patches the server, watches the certificates, takes backups and knows how to restore them. The CMS being healthy does not mean the machine underneath it is healthy.
Write down who holds that responsibility. An agency can do it under a support agreement. An internal infrastructure team can do it. The risky version is the one where both sides assume the other is watching.
Deployments need a habit.
However the site is hosted, you need a way to move a change from a test environment to the live one without copying files by hand. Editors need a place to preview. Developers need a place to try an integration without touching live content.
Ask to see that path before you sign. A diagram with three environment names and no owner is not a deployment process.
Choose for the second year.
The launch is a poor moment to judge hosting. Look at the first year of updates, the first late-night fault and the first time someone new has to publish a page.
Cold Banana delivers Umbraco on Cloud and on hosting that organisations already run. Bring the constraints you cannot move. The hosting decision should follow those, not a default package.