welcome to the forum.
the reasoning for the increase in power is from many reasons. there are different versions of the the K20 head and commonly know by the "brand stamp" or "product code reference" that Honda gives them. The different versions of the k20 head started in 2001 with the PRB-1 head casting found in the Honda Interga Type R (DC5) & Acura RSX Type S starting in 2002. The Honda Euro R Accord was also given a K20 head with the RBC casting the same as the K20z3 head. There is also a better flowing K20 head and that is the RSP port found on the FD2 & FH2 Type R's. All of these heads are designed for higher cfm flow, not designed for low end velocity, and the VE of the K20 head in the higher rpm's is amazing and is the reason it changes the characteristics of the K24 engine helping it to breathe better in the higher rpm's making them suitable for camshaft upgrades to get more power from the K24.
The K24 head is designed for port flow velocity to build TQ faster and quicker to move the larger cars it was intended to serve. It is still a nice head do not get me wrong, just not the same beast for maximum cfm and maximum VE in the higher rpm's. Some companies have developed a port design for the K24a2 head to make it a game changer but head to head the choice is clear.
The VTEC is not more aggressive in the K20 head than the K24 head with both using the three lobe camshaft on both the intake and exhaust side. Certain K20 heads do not have three lobe cams on both intake and exhaust, the same goes for the K24 head.
