The big difference is time. In CS you are under constant time pressure from every angle.
You starve, you get sick, the detective comes after you, you go insane, you go broke, ect.
On and on and on, so every moment counts, sometimes a second doesn't matter much, but sometimes being a single second slower can ruin minutes worth of plans or even kill you if things are tight enough. You have to juggle cards and plan things out and make bad choices.
There is no time pressure in BoH, instead of cards expiring based on seconds everything instead expires/renews at the end of the day.
Because of that everything is more chill and stuff like card juggling is completely out the window.
Instead of frantically trying stuff you slowly and methodically progress a single day's worth of actions at a time.
Exploring the house and looking at everything in the room when you find it, working out how skills work, and puzzling out how to read the next book or unlock a new room without having to worry about everything crashing and burning because you were two seconds slow pausing the game and your maid in the mirror disappeared.
There are a number of UI upgrades, such as the game flat out telling you what item types go in which slots that makes things a great deal clearer and makes discovery feel better since you don't need to check every single space with every possible item type.
Also yeah, so far (5 hr) no death or even any true threats.
Is it better without time pressures/constant fear of death?
Dunno, its certainly a different feeling one, that's for sure.
I can say though that the time pressure and worry made made some parts of CS really fun when things got tight and you barely manage to squeak through, so it isn't just a flat out upgrade.
Personally I would recommend it if you think you would like a more chill CS.
I've had some issues and bad luck with cultist simulator. My first attempt at it was a gimmick ending, followed by a quick death, followed by me picking "the medium" as my first real go at the game, which turned out to be the hardest plotline and required basically going through every card in the game, meaning I didn't have much mystery waiting for me for the rest of the characters. At least I beat that one.
The way permadeath in CS was implemented was a pretty big mistake. Making you restart and do the exact same thing in a long grindy game with no real randomization where you are expected to collect every item in the game simply isn't good design.
My own question - where do you spend normie cash? All i see is spending it on hiring help to clear the rooms, but base income you are given feels like it will be enough for hiring every day, which is poignantly not the case.
Only hiring as far as I've gotten, although you can spend a lot on hiring help. Hiring the priest/smith once a day is easily doable, but the better helpers from the inn are pretty pricey and if you hire them too much you can easily use up all your money. (Also sending a letter costs a single pence).
Still enough areas left in the game that I would be vaguely surprised if there wasn't anything else to spend the money on though.