You have decided to move forward with Microsoft Dynamics 365 Business Central and are trying to decide between 0n-premise or Cloud. Naturally after having done on-premise for 25 years, and then seeing what a cloud subscription brings, the short answer is, choose cloud.
This blog would be too short if I stopped there, so let's state the reasons for cloud first.
No in-house technical expertise required. Think SQL server administrator, OS administrator, Business Central server administration, backups, hardware monitoring etc.
Cyber Security - If your system is accessible over the web, unless you are in the cyber security business, you should delegate this task to the team at Microsoft.
Upgrades - When your system lags behind a few versions because you can't afford the downtime or lack the expertise to perform an upgrade, your users and by extension the company suffer. It's like using an old TV in a HD / 4K TV world. In the cloud, upgrades are automatic and almost instantaneous.
Backups - In the cloud, your data is safe because Azure SQL does an automatic geo-redundant backup, no dealing with hardware loss (like a hard drive failure) and management of disaster recovery.
Reasons to have an on-premise installation
If you require Integration to in-house developed systems, the fastest way to get up and running would be to use a on-premise solution
You have sensitive data that you cannot store on-line in the cloud. Keep in mind, all financial data is important and sensitive, but here we would be talking of data that goes beyond your typical HR or income statement data, think security clearance info etc.
You have been using on-premise BC for many years and are comfortable with all the technical requirements and don't want to transition yet
To recap, create your own list of pros and cons. Too often I find the C suite executive makes decisions based on outdated information. Remember the anecdotal "your data is safer in-house instead of the cloud" isn't true if you factor in all the technical expertise required to keeping it safe. Just like the key man / woman in your company, with on-premise software your IT department is key. An alternative is to use software as a service, you should at-least consider it.