For most people, the only difference is going to be price. With the models we carry, there is a significant cost difference between green and red lasers, so most people end up going with the less expensive option. This is perfectly fine, and most likely won't have an impact on how those people use LASR.
There are a few exceptions to this rule:
If you have two different weapons that you'd like to use in one drill (say, a SIRT AR bolt and a SIRT pistol), or want to use the SIRT pistol's take-up laser while you're using LASR, or want to use the laser color to mark for two different shooters (there is a far easier and cheaper way to do this using Race Mode within LASR) you might want to look into getting at least one weapon with a green shot indicating laser. LASR has a feature called Laser Color Detection, which (assuming lighting conditions are optimal) can differentiate between green and red lasers, and label shots accordingly. You can find more information about Laser Color Detection in the LASR Online Tutorial.
If you're planning on using the laser training aides for force on force, or other applications not involving LASR, (or you are hell-bent on trying to use LASR in an unsupported manner, such as with a projector) a green laser will be the better option. Green lasers tend to be quite a lot brighter than red ones, so they travel farther without dissiptating and don't get washed out by other lights quite as easily. They are also a lot easier to spot for force-on-force applications.