I don't think the west cares about the NX. The 'thirst' for the new gen to hype up their products on and sell is already here and established. They no longer have a need to be gungho with it and that is the simple reality. Unless the western market experiences some sort of catastrophic collapse from over budgeted AAAA productions (or Nintendo pulls a Wii out of its ass), Nintendo will, for this gen's duration at least, be a secondary thought against the established footholds of the X1/PS4.
(If anything, I'd say the west wants to narrow their spread as much as possible in general. Less consoles the better. We may soon see the same thing from the big publishers with VR if the Oculus really does clock in a lot higher than expected on price, with everything funneling to PSVR for main development. Of course, Oculus/Viva have the entire PC community which has already made hundreds of VR capable games, so in this regard such an act may be less than fruitful but we will see. We still know very little on any of the headsets outside of their targets and how comfortable they are...)
Conversely, in Japan, I think developers are trying to proliferate as much as possible in an attempt to survive because two years of throwing titles at the PS4 hasn't turned it into anything even remotely resembling a market leader or even potential replacement of one before the NX launches and the removal of the Vita's crutch on cross-platform titles in that ecosystem. On this regard, and due to the sheer strength that Nintendo has in the domestic market, I think here the support will be considerably better. The 3DS is the only thing sustaining the market (on Nintendo's products and several strong IP from third parties) and nothing in the current market is going to suddenly jump in to take its place. For that reason I think there will be a more forward and immediate attempt to transition the 3DS audience to the next handheld from both Nintendo and third parties. I actually expect to see a good number of cross-gen products from Nintendo, and I still believe there's something in the water for MH:Stories, not to mention DQXI's coming 3DS/NX form.
If the title has western hooks already planted, I expect it to be PS4 first and potential NX. If its the other way around, I expect it to be NX first and then whatever else follows, PC and/or PS4. Or maybe Ninendo will start using Sony's dubious words and start announcing their own "debuts" and PC inclusive "exclusives".
If its a family oriented title, I don't expect another DQB situation to occur, let's put it that way.