Voyager had it worse than Enterprise-D in general, but I am struggling to define "natural disasters" in this case. I'll need help with this as I am not an Enterprise-D expert, but I think I can explain more about what I think is proper context from Voyager.

Strange aliens that invade the ship are just aliens doing what they do. It's natural, but technically not a disaster.

Voyager getting pulled into the delta quadrant was an act of an entity and not really a disaster in the whole scheme of things. It was really bad, but limited in scope.

I almost classified a planet being destroyed by a dangerous power source explosion a natural disaster, but it's not. It's humanoids doing stupid humanoid things.

Voyager does have "Shattered", that seems natural and a disaster, but it's limited to just Voyager.

"Year of Hell" is so close, because time itself is keeping the imperium in a never ending cycle of wiping out entire civilizations, but doesn't make the cut because it was still the work of one crew and the "disasters" technically never happened.

"Friendship One" may be in the running because a civilization was "gifted" with matter/antimatter tech before it was ready. It was a mistake of pure chance that kicked off a path to the destruction of a society.

(Enterprise-D had a few episodes where they were saving planets from actual natural disasters though. As mundane as that sounds, some of those may come out on top by definition.)

Edit: To completely destroy my own attempt to set content, "The Omega Directive" may be it as the Omega particle was able to create subspace ruptures. It's perfectly and evenly tied with Enterprise's "Force of Nature" where warp drives were destroying the fabric of subspace itself. In that context, both win. Unintentional and unexpected natural consequences of one force of nature acting on another. (I just completed wrecked my own previous arguments, I know. Just having too much fun with this one, s'all.)