Sadrik, I personally have never been of the opinion that just because something is a certain way, no matter what that way is, that this naturally implies that the thing is the way it should be, could be, or that it functions best as designed.
I always start with the premise that anything and everything can be improved, or at the very least modified for function, depending upon the objectives of the end-user, complimentary to or in opposition to those of the original designer. (Unless of course it can be practically proven that a thing can only work as designed, that is no other possible satisfactory or superior capability is even possible. This does not also necessarily imply that designed as is is worse than any other possibility, but then again it in no way necessarily implies anything about possible limitations, good or bad. All it really implies is, "this is the way it is and the way it functions at this particular moment in time and under these conditions.")
That being said I've only ever played the chump to god model once, when I first started out playing D&D (it worked out fine in that particular situation), and haven't played it again since.
I don't like the chump to god model, and I didn't even like the dude to badass model, if by that one means a Hollywood type badass who can run 20 foot up a vertical wall (just because he gets up a good head of steam), flip over seventeen times, throw 12 exploding batarangs, shoot fire out of his anus, and dodge a bullet on the way down in slow motion. Personally I consider that type of beads very self-limiting and silly. And mostly boring. But that's me.
I do like the idea of advancement over time, and of gaining capabilities and expertise over time. But as far as a model goes I prefer the Inexperienced Novice to Capable Veteran model. Or the Rookie to Dangerous Man model. And I guess that in some sense the Dangerous Man model could be a badass, but then again he is a mortal and vulnerable, heroic badass, not a superhero badass. (That is to say he is exciting to me precisely because he can be killed like anyone else, and not just because he is so good at killing.) And I reckon that to some extent at least this is a result of my own experience with life, as much as with gaming, and no doubt a function of my age and outlook. And it is probably also a function of the time period I grew up in, and my background, having been both brought up and agreeing with the idea that I don't owe allegiance to anything I feel I can improve upon. But rather it is my duty to improve upon a thing, if I feel I can, and not my duty to approve of a thing just because I am expected to by others. (I've never cared about the expectations of others, even as a kid, and my old man also constantly reinforced my attitude in that regard. My only concern was, "am I doing my best job at this?" If not then how do I change myself, and improve? The same holds true for me about anything and everything outside myself as well.)
As far as D&D is concerned though we don't play it by the book (as structured and written by the designers), but as a redesigned hybrid. Then again I've never played or DMed D&D, or any other game, as written and by the book. To me the game, or any game, is merely an inanimate tool or device open to modification and redesign as I see fit, not a bureaucracy making regulatory demands upon the end-user for the privilege of use or service.
But to answer your question directly I prefer neither model you offered, but that is not meant as a slight of any kind.
Merely a personal observation. They just don't appeal to me, unless by badass you mean a more realistic badass and not a superhero type badass. In that case I'll take your second choice of the two.
I like the narrower style because it allows the GM more room for adventures. In that, a monster you throw at the group is less tied to the PC's "level" - whereas in D&D, goblins are no longer viable threats after, say, 3rd level, and throwing vampires at 1st level PCs may be a bad idea.
What that means is, basically, you can get by with less splat material. Instead of a monster book that details 30 levels of monster (and, say, 20 monsters per level), you can instead have around 60 monsters, knowing that each monster is usable against the PCs for a longer stretch of their overall careers. Which, to me, makes the game seem a lot larger than it actually is... which is a good thing.
I agree with this.