Here's the thing: When you install Windows it loads some generic chipset drivers. Windows uses these drivers to communicate with the motherboard and these drivers "tell" Windows how to access the various features on it - RAM, PCI/AGP/PCI-E, hard drives, etc. You could just stick with these generic drivers, but if you want to use the advanced (or - with newer motherboards - even basic) features of your motherboard (or have increased performance and stability); you will need to install the chipset drivers for your motherboard.
When you hook up a hard drive with an existing Windows install to a new system, consider yourself lucky if you get it to boot into Windows. Most chipsets are so different from each other that they cannot work with another chipsets drivers and will give you a nice relaxing blue screen. The fact that you were able to boot an existing installation of Windows on a new system says that the chipsets from the two systems are similar.
Technically you can install the drivers for the new chipset and continue using the existing install; but then you compromise system performance and stability. No matter what you do, traces of the old drivers will linger and "get in the way". I recommend reinstalling Windows every time you get a new motherboard model (even if they have the same chipset) to get the best possible performance from it. If your old Windows install boots with the new system, think of it as an opportunity to back up your data before reinstalling.