Answering your question: "How do you prefer videogames to handle death or failure?"
My personal preference is like in old games, where, if you fail, you had to restart the level.
Some games like "Black" in the PS2 era, had huge levels with distant checkpoints, and to me, it was a masterpiece, even with checkpoints.
Depending on how long a level is, it might be annoying to restart, though. The developer need to balance this well.
That's why I love roguelikes, but can also enjoy other genres.
Terraria is a good exemple of difficulty choice in this because you can create all kinds of characters. Because if you die, you will always return to the first spawn point. Depending on the difficulty you choose for your character, you will lose either money, items or everything and your character will be deleted (permadeath).
Another good exemple of a good combination of old & new is Monster Hunter series, where you have Hunts. If you fail, it's over. Take your equipament and restart the whole hunt. Love that.
Now, talking about Open World games, I rather have something like "If you die or fail, you lose your progress until this place/region/mission/checkpoint/last save game."
If it's an Open World RPG, I prefer it to have permanent consequences with good writing, after all, a good RPG is made of choices and consequences of choices. If there is no failure or victory consequences, story-wise, it's not an RPG, it's an action, adventure, shooter, whatever, etcetc
Mount & Blade series is a good exemple in this one. Your character won't die (permanetly) but taken prisoner, lose items, money, and such consequences affect your character progress in many ways, like exp gain/loss, renown, honor, you lose troops, many times you lose relations with lords and kings, etc. It's a good balance in my humble opinion. A "True RPG".
As this question is based in personal opinion, this is mine.
darthspudius: Quick load. Life is too short for that perma-death crap.
I understand that you might be joking, but, some people find much more fun in improving all they can so they won't die again than simply "restarting with everything in the last checkpoint." Which is not necesserily bad, it's just personal preference, as I said before. All based in fun.
Take Cyber Hook for exemple. That game is growing in the speed run community. Very fast paced. You die, restart from the beginning in less than 3 seconds. Level based, focused in improving all your tactics, etc.