I don't think there's a good answer that applies to all software packages or situations.
Rolling releases are more risky as there is no predictability around when things will change. You may have installed the thing last night and already there's an update to deal with. But what does that update do? Is there enough information to know if you want it? Sometimes, but it depends entirely on the developer/company releasing the package.
Some things to consider before going with a rolling release package:
- Who are the primary users of the package, and in what environment?
- What is your tolerance for risk?
- What is your process for performing upgrades?
LTS releases are intended to be used for longer periods of time and often have published lifetimes that enable you to plan and test migrations to the next LTS release well before updates to the package/system end.
My recommendation is that servers (with the exception of sandbox/R&D machines) should use LTS releases. On desktop machines it depends on the end user and what that individual wants.
In fact, I would go so far as to say unless there are specific and very good reasons to go with a rolling release, always use LTS releases.
When dealing with higher-ups, appealing to their desire not to spend money is always a good tactic. Rolling releases are more expensive in the long run when you consider the amount of time spent by employees testing, installing, dealing with bugs from new versions, etc. While you'll have to do some of this with LTS releases, their longevity means it's significantly less.