Well . . . you got me :shrug:
Yeah, the term "brighter" can mean different things depending upon the context. Without going into the long version (
click here for that) there are two functions when it comes to the "brightness" of a light. One is the light's total output, measured in lumens, which indicates the sheer quantity of light created with no regard for where it goes. The second is related to the intensity of light, measured in lux, which gives an indication of what you can actually see in the form of light reflected back from your target.
From what you described, you need high(er) lux in order to compete with the ambient lighting from the sun. Because they use optics (lenses) instead of reflectors, the EB1 and EB2 have more intense beams than similarly sized reflector-based lights with the same levels of output. This doesn't mean that reflectors can't make a tight beam, for example the ArmyTek Predator mentioned above has a MUCH more intense beam than either of the SureFires, but they are typically much larger than the optics-based lights. I mentioned the EB1 and EB2 because they are relatively compact.
The beam profile can also matter because, as eebowler mentioned, a light with a bright spill can also hamper your ability to see well because it can reflect light back to your eyes from the sides of the well, making it harder to see the bottom. The G2X you mentioned has a nice general purpose beam but much of its output is in the spill beam where it's of less use to you, or maybe even detrimental.