Two Briggs engines same displacement, physical size, different HP.

I have the following two Briggs engines.
1) Model 445877
and
2) Model 407777
 
Both have the exact same displacement.
However 1) is listed as 24HP, while 2) is listed as 20HP.
 
Is it only a carburetor efficiency difference or is there severely different changes such as cylinder head shape difference which gives (1) 4 more hp ?
 
What i want to see is if I cannot make changes to get the 20HP (2)  to 24HP, so I can use it in the same riding mower as they are otherwise basically identical.
 
 
 
 
 

That 4hp makes huge difference on a zero turn. These 24HP Briggs engines are rather soft, and tend to bend valves.
It used to be marketed as a 27HP until there was some class action suit, and it is is now marketed as a 24HP, so there are serious ethical issues with this particular engine to boot.
At the time when mine bent valves, I replaced it with a 20HP Kohler as there were no 24HP version available at the time.
The Kohler is the better engine by far, way more rugged and reliable,  but the 4HP less is noticeable.
 
I want to replace the 24HP Briggs on another Swisher zero-turn, which bent valves the exact same way, with the 20HP Briggs but want to see if I cannot at least get close to 24HP as described in my original post. The 24HP Kohler costs north of $1500, so that is not an option at the moment, so I am stuck with Briggs.

I am starting to wonder if the 24HP Briggs is not really a 20HP pushed past it's limits, therefore bending valves. They were dishonest marketing it as a 27HP, so why would they be honest about it being a true 24HP either, especially regarding strength of materials.

Why Briggs issued such unreliable engines I dont know, probably an attempt to outpace the competition at the cost of reliability,  but they are horribly soft engines not worth the money.
 
I will look through what you sent thanks.