Personally, I think bang the dice game is overall a better experience. The end goal is the same regarding the roles, but instead your actions are restricted to what you roll, with a push your luck mechanic that allows for rerolls while keeping it a risk to do so.
Because there are no items, you don’t end up in the situation where the sheriff is sitting behind both a hideout and a mustang, flanked by his deputies, unreachable by card steeling mechanics and making it harder for other players to make an impact on his health. While arguably the lack of card combos eliminate cool moments like unloading a ton of saved up bang cards with a volcanic, it also leads to the biggest improvement to game: the games end more quickly so players don’t sit out as long. It is also, significantly easier to teach and learn, so it’s easy to get it to the table with large groups.
I take issue with the first description of the first one. It is an evolution from what was courage wolf. Courage wolf was a meme template where the top line set up the situation and the bottom showed how you courageously did something in response.
People then took it to the next level with insanity wolf, the one depicted here. The top line is the same, setting up some kind of situation. But the bottom line changed to doing something absolutely insane that no person would ever ever do in real life.