Not sure if there is any documentation from Jamf on this. There might be. But in general, the main differences are (not an extensive or exhaustive list)

Accessibility
Cloud - accessible from anywhere over the internet. Can't be locked down from outside connections other than through the use of 2FA. This could be a problem for InfoSec folks, but since so many services are now cloud based, most places are OK with that kind of setup.
On-Prem - can be internal only, or accessible over the internet as open or with restrictions if set up behind a load balancer.

Upgrades
Cloud - Depending on the number of seats you purchase, you may not have any control over the upgrade schedule to new versions of Jamf Pro. Unless you are a very large customer and have a dedicated hosted setup, you will be upgraded on Jamf's schedule.
On-Prem - control over your upgrades to Jamf Pro. You do it when you want to, so if you want to stay on an older release for some reason, you can.

LDAP connection
Cloud - Not as easy to to connect to your internal LDAP environment (if you have that). It can be done with Jamf Infrastructure Manager (JIM), but involves a little setup and having JIM run on a separate server.
On-Prem - generally easy to connect to your internal LDAP environment with no extra tools or services, for logging in to the console and also doing LDAP user info lookups, etc.

Database access
Cloud - No access to the MySQL database.
On-Prem - Full access to the MySQL database if you need it. It also means you must maintain it (run repairs as needed), back it up and upgrade it when needed. (see above on "Upgrades")

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Outside of those main ones, you may also see some performance issues with a cloud instance that you may not see with an on-prem install. But that all depends on how many resources you throw at your on-prem install. Performance can be poor with an on-prem setup if you don't spec it out correctly. So that's something to take into account also.

Generally speaking, I recommend people look at cloud hosted. It kind of takes a load off of you or someone on your team to maintain the server(s) and environment. Jamf handles that all for you so you can just concentrate on the work you need to do to manage your Apple devices. But some people like the extra control that on-prem provides them with. It's kind of up to what you're looking for.

Of course, you do pay a little more with a subscription hosted setup I believe since you are also paying to have Jamf maintain your instance from the backend for you.

Hope the above helps. If anyone runs across a document that details all the differences between the two, I'd also like to see it, as it would be handy to have when talking with customers looking at the product.

@mm2270 Do you possibly know the price difference between Jamf Cloud and on-prem. I originally agreed on cloud, but decided to switch it to on-prem last minute for several reasons... I believe my invoice was billed at the cloud rates but I have to double check.

@jared_f I honestly don’t know and, I could be wrong that there’s even a price difference. It might just be that the cost is divided up in a subscription model with cloud vs a single payment per year with on-prem.

That being said, don’t take my word for anything since I don’t work for Jamf and would not presume to speak for them. Contact Jamf about it and see what they say.

When we first bought Jamf in 2013, the cost of the SaaS option was a lot more than on-prem, so we opted for the latter.

We're currently awaiting our renewal quotation but I've been told by a few that the cost now is pretty much the same, so I suspect we'll be migrating to the cloud before long.

Jamf emailed me back today and the pricing is now the same for on-prem and cloud.

Honestly, it really comes down to how much control you want. At least for us, I need more control over when I upgrade the JSS.