Controller Configuration
The Wii Zapper utilizes both the Wii remote and the nunchuck to fit into a case that looks like--when it's all put together--a Tommy gun from a Dick Tracy comic. This way, players can aim the Wii remote like they would a rifle and have easy access to the nunchuck's analog stick.
The Wii Perfect Shot only fits the Wii remote into its pistol-like apparatus, so the nunchuck remains separate from the device but can still attach to the remote through the handgun's handle.
Trigger
The purpose of both accessories is to help aim the Wii remote and fire the B-button trigger like a trigger on a gun. For the Wii Zapper, the B-button on the Wii Remote fits into a trigger on the accessory for players to press. The trigger on the Wii Perfect Shot, however, pulls a spring-loaded slide that presses on the Wii remote's B-button, which is closer to pulling a trigger on a real gun.
Wii Remote Button Access
Some shooter games require using other buttons on the Wii remote aside from the B-button, and the Wii Zapper makes it a bit more difficult to access any of them with its two-handed layout. Since the Wii Perfect Shot is light weight and can be held with a single hand, it's far easier to reach any of the buttons.
Aiming
Since the Wii Zapper has a two-handed design, it's easiest to aim from the hip, which detracts from accuracy. It can be held up like a rifle as well, but the Tommy gun style doesn't make this very comfortable for long. The Wii Perfect Shot allows players to aim with the fixed sights on the accessory, so players can aim like they would a handgun (like a light gun) and with far more accuracy.
Manufacturers
The Wii Zapper was developed by Nintendo, and as such, is the accessory it promotes and urges players to use. The gun accessory comes packaged with the Link's Crossbow training, to help teach and orient players how to use the Wii Zapper efficiently. The Wii Perfect Shot is a third-party product developed by Nyko and does not receive any support from Nintendo. As with any third-party product, there is always the risk of the accessory not working properly with the Nintendo Wii system.