Note to people: To those whom are dancing around the issue, this thread is about the Brawler's in a real-life setting, NOT the game setting. If you cannot agree to or understand that, then this thread is not for you.
Well, if considering them in a realistic setting, Charizard has the obvious advantage of flight, meaning that Charizard can gain a good low angle of attack against Bowser in the air, and do something like bomb raiding Bowser with boulders, and use his fire-breathing abilities against Bowser. He also has smarts, though limited in reality, he could form complex strategies, that to us would be simple at best, but possibly effective. Charizards tail should also be considered because it takes a good amount of muscle to make it straighten out and be used as a stabilizer in active flight. So in an air battle Charizard could possibly have Bowser on the ropes...However, realistically, Charizard, despite the advantages he does have, does not have a chance.
Bowser is 10' 0" feet tall, and thats pretty big. Charizard is about Bowser's height thanks to his long neck, buts about it in terms of height. Bowser has many advantages despite being grounded, that give him the upper-hand in this fight. Also, to call Bowser dumb isn't exactly accurate, while he may not be the brightest bulb in the room, its doubtful that he can't come up with any strategic ideas of his own. The fact they both breath fire negates that as a viable option for the both of them as well.
Bowser's shell, like any turtle-dragon hybrid, is his best tool for survival, Charizard could try dealing attacks against him while he is in his shell, but for the most part, the point would be moot, as it can be shown that Bowser's shell is quite strong, it would take probably take a large-sized object at terminal velocity to even crack it, it looks that strong, the spikes on his back also aid in defense, making the use of such a tactic null and voided, although the spike would be dulled most likely, so the use of rocks as a way to kill him by breaking his back (because a turtle/ tortoise's spine is connected to their shell), would not be too effective, and the most it would would probably do is give him a sore back for awhile.
Bowser's physical strength is also a deciding factor in the fight, which is probably more than that of Charizard's own by a country mile, Bowser's physical build suggests a great amount of this physical strength, and looks like a terminal velocity punch (By that I mean the maximum speed a punch can be thrown within physical limits) would send something as big as Charizard backwards into the air, or if hit in the correct spot, kill Charizard instantaneous by crushing of the skull, breaking of the neck, spine, or ribcage, and any other place that could prove fatal.
His claws also make matters worse for Charizard, as despite the fact Charizard would be faster at using using his, the size of Bowser's own claws would likely make a big enough gash in him to make him bleed into his stomach, or worse, completely disembowel him, which case Charizard would die in less than sixty seconds if not ninety, chalking up another disadvantage for Charizard.
Now, we all know that sometimes Big = Slow (In the animal kingdom, this is sometimes not true. A Rhinoceros for example can gallop along at around 25 miles per, not too shabby for an animal not too far under the size of a Chevorlet pick-up; and an Elephant, the largest land mammal existing on the planet right now, can stampede along at the same speed if it is frightened or upset, pushing itself to the limit to chase or flee. Bowser, while he would not run very fast at all due to his weight and inadequate legs, would probably do just fine with walking or trudging along. Charizard however has no speed advantage on the ground either, as his legs are the same as Bowser's in terms of length, making them inadequate for running as well.
Bottom line, if it came down to terra-firma-based combat, Bowser would likely be the winner, and Charizard's odds would only strengthen so much in the air.
My vote therefore goes to Bowser.