I've played only the GK Neo 112-II - not the 1x15. But I would say that, in addition to having a little more power handling capacity, the Neo 115-III is going to handle the deep lows a little better, and sound more open and more relaxed while doing so.
From what I've gathered, the GK Neo 115-III is one of the more balanced commercial 1x15 cabs on the market, with a frequency response with goes well up into the upper midrange (before crossing over to the horn), while remaining surprisingly punchy for a 1x15. You might like...
MM