These scenarios are identical in my opinion. They'll likely dwindle and die in a short time anyway. The wealthy are not particularly well suited to rebuilding society, nor are they at a disadvantage, they are just average people who (used to) have wealth.
Actually, little side thought occurs to me here, they can't access their wealth unless it was stored physically, and even then, only if our concept of currency hasn't changed. In my version of this scenario, I'm assuming the 1% still have useful currency, banks still work, etc.
So we got a bunch of more or less equally rich people, who may have access to resources, but their laborers and security forces are Thanos-snapped away.
Hmm..
My guess is that the ones who have weapons will establish a sort of warlord apocalypse scenario. Wouldn't be much different from any other random selection of 1% of the population. The resources you hold and the skills you know matter even more when society disappears. It will start with 1%, the sudden shock of not having most other people to provide for each other will quickly halve that. The fighting over resources will kill a bit more. Eventually there will be an environmental disaster like a drought, and that's it for humanity.
People run technology. People have knowledge. These things die when people die.
The richest 1% are not those people. We'd have a better chance with a random selection (only 12% of billionaires are female!)
The internet, electricity, running water, sewage, do not work unless someone is operating and maintaining them. Manufacture of supplies to maintain them depend on coordination across the globe, and further specialized skills.
Effectively, technology will be reset for at least a generation to pre-electricity levels. This is survivable, sure.
But, the way I see it, if this event happened instantly or close to it (months, even) the survivors would not be prepared to shift immediately to that lifestyle. This is where I would predict mass deaths.
I've also been assuming these people are not together in one place, and without air travel they would be limited to a shorter range. I suppose if they were all smart enough, they might congregate in a few different places. There's a chance if they cooperate and don't fight each other. Humans can do that. The richest humans, though?