"Will a boat that heaves-to just find with a large genoa under light winds have different characteristics heaving to under heavy winds?"
Yes. How a boat handles is a complex set of three-dimensional balances. If you stick a pin down through the deck and hull, parallel to the mast, the forces pushing ahead/behind that pin will rotate the hull around it. That's one center of balance, for the forces pushing on the sails (and the freeboard, the exposed area of the hull above waterline).
The mast may or may not be near that center of balance on a sloop. But as you change the sails from big light air sails to smaller storm sails...the balance point shifts as well. Especially as the big genoa changes to a storm jib and the force probably moves forward.
At the same time, there is another center of balance for the hull and keel, resisting rotation and sideways motions of the hull in and against the water. And as the hull heels over, that one will change too.
With all the motions and changes, boat building is still something of a black art because you can't just sit down and balance one set of factors, you need to compromise them all, against all the others, at each different speed range, heel, etc. A really good [read: experienced or lucky!] designer can find some sweet spots and design a boat that is sweet and well-mannered in a wide range of conditions, but just looking at two boats at a show...you or I would never know.
So, reputation for the designer and boat are something to consider. And then getting to sail on one, to see how it really handles in different conditions. There are "horses for courses" and no one design does everything equally well. Part of that is why some boats will have a reputation as good bluewater boats, that are also kinder in rough wx, while others are great liveaboards--in sheltered waters.
Which goes back to Sailaway's original comments. Dunnage doesn't come with a boat, it isn't a structural part or a component. It is up to the skipper to load "equipment" on board including damage control supplies. Some boats, like an Islander36, may have a huge open companionway that makes the boat nice and light, airy, roomy when below. Arguably a good boat--but one of the first definitions of an "offshore" boat would be a wee narrow companionway, which is structurally stronger and easier to secure in a storm.
Losing a hatch on a sailboat is probably rare these days, when they are properly dogged and secured. Lash a dinghy onto the hatch (a load it was never made to endure) or leave it partly open (so green water can get under it and tear it off) and the problem is not a bad hatch--but human error.
The recent loss off Chile apparently was more complicated than that, from the many comments and long discussions what really didn't make it out on the news was that the mast came down ON the steering pedestal, incidentally making the boat impossible to steer. Add a hatch failure (for whatever reason) and a battery bank breaking loose (again, for whatever reason) and a medical problem (reported as a leg cut to the bone)...
Well, that's the ocean. Things can often get much worse very quickly. Not making the first mistake, or being able to respond to it, requires skill, experience, and luck.
"mentioned in the boats's characteristics papers? " What's that?
Something mandated with new boats in the EU? Remember, here in the US no one rates them by offshore category, it is "here's your boat, where's my money?"