For laser sights (sights that actually put a laser dot on the target--not optical dot sights) there are limits to the allowable power output to insure that they are eyesafe.
Those limits are stated in terms of pure power output--milliwatts. But it turns out that the human eye is quite a bit more sensitive to green light than red light. So a green laser at the same power limit will appear brighter than a red laser. This turned out to be useful because in bright conditions, a maximum power red laser usually isn't visible while a green laser at the same output power level shows up better due to the human eye's higher sensitivity at that wavelength.
The second issue (again as it applies to laser sights, not dot sights/holographic sights) is that red LEDs tend to use less input power to create a given amount of output power so green lasers tend to use batteries faster than red lasers.
BUT, that's not what was asked about. The question was about a dot sight--an optical sight with a dot reticle--not a laser sight that puts actual light on a target.
In that case, the output power is not an issue--you can turn the dot reticle up to a brightness level that is going to work for nearly any conditions--regardless of color. You're not fighting the same kind of legal power limits as with a laser sight so the color choice should be made on personal preference and/or application. If you're going to be shooting/aiming at a lot of reddish/orangish things then maybe a red dot is not ideal. If you're shooting where the background tends to be subdued colors, maybe red would work better.
And because the power output required to make a dot sight work is so much lower than what is required for a laser sight, battery life should be essentially identical for either color choice.