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.

It's good! It's basically exactly what you're describing: a paired down dice version of the original. It plays a lot faster, which is a big plus, and it's rules are simpler. You do lose something in the process, some of my friends missed all the shenanigans with guns, horses, and TNT

I have great memories of the dice game. It's great for three players, too. It's also easier to explain to people

I think it vastly improves on the card game. The dice bring a "pick up and play" element that was missing from the card game because I was always spending half of every game explaining to players how the cards work. Bang Dice was everything I wanted; the push your luck element amps up the fun in a big way, and the removal of hand management cuts down on analysis paralysis. It's fast, fun, and a perfect pub game.