Everything, absolutely everything depends on for what you will be using windows 10 for.
Is it for testing purpose, or daily usage purpose, gaming purpose, business purpose, a back up os, auditing purpose, likewise depending on the needs, there are tons of purpose and uses of windows version.
For instance, for daily usage purpose, windows 10 Home would suffice but there is no rule stating that you shouldn't install windows 10 LTSC/Enterprise Edition for home usage.
So, it all brings down to the question, what you are going to use the OS for.
My take on Hospital using LTSC release is, they don't need updated software to work for them. For doctors and medicial department, PC is something that sorts out their bulk files of patient details and their records that usually takes up halls of papers. So, they don't care if they are outdated to the current version if they can have a single version that is most stable and does work for them that want it to do. Thus, as long as the windows performs what they want i don't think they would raise an eyebrow if it is pro/ltsc/enterprise. For them, PC is just a tool to make their records easier, they have lots of other things to worry about, like patient.
As for Pro & LTSC difference. Apart from obvious stable kernal. The other thing is how quick the updates are for both.
You may get a update for every little thing in as quick as every 4 weeks for Pro version.
There maybe quarter/Half/Yearly updates depending on the integrity of the OS for LTSC.
Pro gets your system updated to the latest version available.
LTSC gets your system use the most stable version available.
The reason why it is called a LTSC is because the same version of LTSC in other version maybe old and patches for the version would have been stopped. But you will get the latest Medicines available for the LTSC as long as the servicing period remains.
Bottomline.
If you need a PC with latest updates, Use Pro.
If you need a PC with install and forget about the OS, use LTSC.