Short answer, larger diameter lenses with longer focal lengths produce lower divergence. The larger the lens (as long as the focal length is right not to under, or overshoot its diameteter by a large amount), the lower the divergence. You would have lower divergence, even if you overshoot 50%, but you would also loose half the power.
The G8 has about a 8 mm focal length, the longer the focal length, the more the beam from the diode will expand into a thicker beam before it reaches the lens producing a larger diameter beam. Once collimated, a thicker beam diameter will produce a lower divergence beam.
Some models of diodes have outputs which expand at such a fast rate that a lens with a long focal length can cause some amount of truncating, or blocking some of the beam from being able to get through, as the beam diameter can be larger than the lens is.
The NUBM44 is potentially one of those diodes, there are members here who have a lot of experience with that diode using different lenses, perhaps one will chime in with more info. The G8 might be fine for that diode, but I'm not sure.
In my view, a tighter beam means better pointing, and low divergence produces a tighter beam at distance.
All depends on what you want to do. If you want to correct it to a square beam or live with a bar at distance or are focusing to a spot. Different answer for each. Go glass not plastic at the 1w level. Welcome post who you are in the new member section. Post what you want to do here.
look up cylinder lens correction, prism correction for making beam a spot and or square. I have to go to work sorry for little detail.
I don't think he was concerned about beam shape, but with a laser diode a square beam shape would be better, for sure, then less fast axis expansion than without it. That brings me to recommend a DPSS laser with a beam expander on it instead.
We can make things work well, all it takes is time and money, but where did he go? I swear, some of the time I think these guys are generated to ask questions when the forum gets too slow etc. Only the shadow knows.