I have been playing Bowser since Brawl launch, and Charizard since Smash 3DS launch. I am very good with both characters, and I can tell you that some of the things you said are wrong. I agree that Bowser has superior tilts, aerial attacks except for Nair and Uair, and a better dash grab. However, Bowser, just like Charizard, is
very reliant on the Neutral B in the neutral game/approaching, especially against extremely projectile-reliant characters, due to the fact that this move is safe on both shield and spot-dodge, unlike most of the other moves of these two characters. Also, while you said that Bowser's out-of-shield game is only very slightly better than Charizard's, I disagree with this, and believe that the out-of-shield game is one of Bowser's most notable and significant advantages over Charizard, not because Charizard's out-of-shield game isn't very good, but because Bowser's Whirling Fortress out of shield is simply a god-like option.
While Bowser undeniably has many advantages over Charizard every here and there, I believe that at the end of the day, the following advantages of Charizard's outweighs all of Bowser's advantages (in descending order of importance):
1. The fact that the entire length of Flamethrower flinches, unlike the case with Fire Breath. This is the most important reason not only because of the reasons outlined in my previous post, but also because it makes Charizard far better at edgeguarding than Bowser. The details of why are outlined
here.
2. Charizard's jab is faster, and since it consists of three hits, has the option of possessing a longer-lasting set of hitboxes, which is better for frame-trapping/"counter-punishing" purposes, as outlined in
this post.
3. Charizard has a much better and less situational kill throw.
4. Bowser does not have a move whose function (in terms of the combination of its damage, knockback, hitbox size and situation in which it would be used) is anywhere close to equivalent to that of Charizard's Dsmash - a very important and useful move in Charizard's arsenal.
5. Flare Blitz
6. Charizard's standing grab is faster and has more range.
7. Charizard has three jumps, making his movements through the air more flexible and his landing less predictable.
8. Charizard has a higher dashing speed, which not only further contributes to the superiority of his neutral game, but also his punish game as well.