The reason for a given powder charge that a 180gr bullet will have more KE than a 150gr bullet is straight physics.

On any firearm and load, the powder charge is not completely burned and fully expanded before the bullet leaves the muzzle (muzzle flash and report). Any gas expansion or powder burn that occurs after the bullet passes the muzzle is lost energy.

Given that, the 180gr bullet has more mass its acceleration will be slower than the 150gr bullet. This will result in more time for the powder charge to burn. This extra time between the 180 and 150 muzzle exit times allows more powder to burn and expand behind the 180gr bullet than the 150. (thus more energy is available to push the bullet), also resulting in higher sustained chamber pressures and more area under the pressure vs bullet displacement curve than the 150gr bullet. Because of this your 180gr bullet has more KE leaving the muzzle than the 150gr bullet.

The difference between the bow and the gun is the bow expends all of it's potential energy into the arrow. The gun has excess energy that is wasted at the muzzle. To make an apples to apples comparison between the bow and gun, you would have to reduce the powder charge so that the powder was completely burned and the gas had completely expanded by the time the bullet left the muzzle. In that condition (fully burned powder = constant KE produced) both the 150 and 180gr bullet would have the same KE at the muzzle.