The one single/main benefit to a green laser is going to be daylight or bright room light performance on the target. And if you need that, it's a big benefit.
If it's for low-light/night use a green is bright enough that the spot can actually ruin your night vision if it's on something close to you, and even a 5mW beam is bright enough (human retinal response is roughly 20x stronger to green than red for the same milliwattage/power output) that it can be seen from the side, and can possibly give away your position easier.
Greens are more expensive, because they're more complicated and more fragile. So making one that stands up to the rigors of firearms use is more difficult.
A red laser, it's just a solid state diode, and a lens.
A green laser is an infrared diode that's many times more powerful than the final output power, because of all the losses that will happen in the subsequent steps.
The IR laser light from the pump diode goes into a crystal that drops it to an even lower IR frequency by it's atoms absorbing the IR light, then re-lasing it.
Then the lower IR laser goes into a second crystal that absorbs it, and re-lases it as visible green light.
Then the beam goes through an IR filter (if it's a properly made quality green laser device) that cleans out any residual IR light that's leaked through both crystals.
Then it goes through the focusing lens.
Granted, this is all in a module that's still the size of your first knuckle of your pinky finger, but it's many more steps. To produce just 5mW of 532nm green light, the source pump IR diode may need to be as much as 500mW in power. This causes more waste heat, and also drives the batteries harder.
The alignment of the crystals and all the parts also makes the green laser very heat sensitive. So cold and heat can vary it's power output greatly.
Single stage green diodes that would be much simpler like the common red diodes are poised to enter the market soon. Things like laser pocket video projectors for smartphones etc. are driving their development, although it's not yet clear to me if the beam will be suitable for pointer use. Some diodes produce very neat colors, and some at very high powers, but the beam specs are awful, like a flat "-" dash shape that fans out very quickly no matter how well focused it is. For instance, 1000mW blue laser diodes are now common among the grey-market Chinese sellers, and hobbyists, but the beam specs are horrid for long distance pointing. It's a friggin "light saber" but it produces a fat blobby rectangle at any appreciable distance of more than a dozen yards or so. Corrective optics are possible, but adds to the weight and complexity, and can rob you of as much as half the output power. Also, the blue diodes in this example, they won't even lase at an eye-safe level. IIRC, the don't even produce a beam at less than 50mW. Enough to possibly toast a dot into your retina permanently.
So no telling yet if the new generation of green diodes will be suitable for aiming lasers any time soon.
Since you're posting this in the night vision forum, is there a night vision system you may be using this in conjunction with? NV's sensitivity to certain wavelengths varies with the tube and technology type, but most trend a bit more towards the red and near-IR end of the spectrum in their sensitivity curves, but I'd suspect either a green or a red would show up well, or possibly even be too powerful depending on the type of device you'd be using it in conjunction with.
A low power IR laser that's like 1mW or so is best, since the NV is so sensitive already, and better if it's not a newer device that has the auto-gain and various protection features if the spot accidentally lands on a nearby object and blinds the tube.