From my experience in the past, ups are done to be constantly on, and as far as I know, usually they have failsafe mechanism in case something is not working as intended. Laptop batteries do not have such extensive protection from what I know. However, if an ups is getting old (around 5 years or so) is probably best to change the batteries (if the model allows it)

Laptops use lithium-ion batteries and (at least your Average Joe's and majority of commercial units too) UPS uses sealed Lead Acid. If lithium ion battery goes belly up it'll burn your house down. If lead acid battery does the same, at worst, it'll leak a bit of corrodive fluids to whatever it's on top of.

There's commercial size li-ion UPS's too, but they require quite a lot of hardware around them to be used safely. Search from youtube (or whatever you like) a cell phone battery explosion and then scale that up to a fridge-sized cell-phone. It's quite a bit of steel and concrete to contain that amount of energy. And the funny thing about li-ion fires is that lithium ions reacts quite violently with water and the battery contains all the chemicals to keep the fire going, oxygen included.

So, yeah, UPS is a whole another thing to manage than a laptop battery.