Say it is a Vita refresh.
This could do a couple things around the edges that could hurt NX's chances of getting wide developer/consumer support in Japan.
By providing a short term boost in Vita sales, such a move could make PS4/PS3/Vita cross-gen look like a bigger ecosystem and there'd be less impetus to port to NX early on, which would hurt NX's potential catalog and, therefore, adoption. Similarly, if the refresh was beefed up somewhat, more games could be cross-gen between PS4 and Vita more easily, again lessening the impetus to port to NX.
I don't think a refresh could kill NX in its crib (it'd be crazy to think so; if NX is stillborn, it is a combination of Nintendo and mobile that killed it), but it could drive a modicum of support away, which is something that Nintendo really needs to stop having happen. NX is Nintendo's opportunity to corner what remains of the Japanese console development community, which in turn drives up their consumer base through more software. Every potential multi-plat from PS4/PS3/Vita crossgen that Nintendo loses out on is a blow to NX; not as big a blow as losing 3DS support to mobile, but a blow nonetheless.
Say it is a PSP3, with similar specs to NX. Unless Sony has bought off Nintendo's 3DS support and developed a new IP that can compete with Nintendo first party on handheld, this will do worse than NX against mobile in Japan. Perhaps if it has cool compatibility with PS4 and NX does really bad in the west, it'll do better than NX in the west as another NEO/VR for the consumer deep into the Sony ecosystem.
It'd also have the potential to keep some third party support from NX that NX could have otherwise received.
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Ultimately though, such a device will not be a huge deal for NX, but could make the environment it launches into less than ideal. Mobile is a much bigger threat to NX. That said, what I'm saying is not relying on the hypothetical device doing well or doing better than NX. Rather, it is assuming quite the opposite, which I think is the safer assumption. It is what damage I think the device could do to NX's potential even taking into account that the NX will likely outperform it, whatever that amounts to.
Basically, I could only see Sony doing this as a move to lower the ceiling on NX as much as they can in light of the Vita's failure. It wouldn't be a move to build a handheld future for Sony, but rather to constrict the change a hybrid Nintendo could bring to the gaming market and development community, particularly in Japan.
Sony's future doesn't rely on Japanese consumer or development support, unlike Nintendo, but perhaps they would still rather not share what they do have in that country.
