In terms of how they track, balance, as well as their hulls relative strengths.
The same is true of various keel boats.
I have no idea what combination of errors caused that grounding. Those rocks didn't shift like some "Riddle of the Sands". Having had my share of Close Encounters of the Fourth Kind with fixed extensions of the Earth (and some attached, but floating objects), I suspect that there is no good explanation for most such occurances -- maybe just reasons, maybe just excuses. ;^))))
The nibble handling abilities (i.e., the cabability to quickly steered out of harms way); and, the tracking characteristics (i.e., the likelihood that the boat is going closer to where it is pointed) of full keeled and very full bodied boats can contribute to such occurrences or the capacity to recover before they become more notable.
There are a number of fin keel boats that run aground and are lost or badly damaged. I similarly have seen examples of full keeled boats that have been in like circumstances.
I can understand the belief that pulling a boat off of a very severe grounding probably would work better. But in most cases short of a really hard and severe grounding, I would rather try to pull off a vessel with less contact area. All fin keels aren't created equally, just like all full length keeled vessels aren't also.
On rocks like the crew of Aurora deposited here, I'm not sure the type of underbody after the grounding a occurred was all that material.