If you have calibrated your displays, then using same model of monitor wouldn't solve the problem. Each monitor would need its own corrected colour profile loaded.
The problem exists in Windows XP. It appears to also affect Vista & 7 (although some sources imply it doesn't). I'm not sure about 8. The solution is to use 3rd party software to automatically load the colour profiles.
The calibration software for your colourimeter (or photospectrometer) will probably take care of loading the correct profile to each monitor. If it won't let you calibrate multiple monitors (without paying for an upgrade), you may be able to overcome this limitation be calibrating the monitors one at a time (disconnecting the others if necessary), then using a 3rd party utility to load the profiles, taking care to match profiles to monitors.
If you have not calibrated your displays and are just using the manufacturer's default profile, then having the same model avoid the problem. But it is well worth calibrating your displays.
If you don't have a hardware calibration device, go to Control Panel -> Colour Management -> Advanced -> Calibrate Display. This will take you through some tests to try and set the correct gamma (like the old Adobe Gamma utility). It is no substitute for proper calibration using a colourimeter or photospectrometer, but it better than nothing.
Apologies to Dean if I have gone a bit off topic. :flower: