Qualcomm's success in providing phone SoCs is almost completely tangential to what makes a good handheld console chip, though. They're popular because of the breadth of phone-oriented hardware they integrate right on the die, which allows OEMs to minimise their time to market (a big deal when some customers like Sony have as little as a 6 month turnaround on new flagships). They're typically beaten on the graphics front by the PowerVR-powered Apple AX series. And although Adreno is technically branched from AMD's GPUs, they will have diverged so far apart by this point that I can't imagine there'd be any worthwhile advantage over any other mobile GPU in terms of cross-development with an AMD home console.
My vote's still with AMD for the handheld chip. They might not compete with something like PowerVR at 28nm, but they don't need to. Take Mullins, swap the Puma cores out for ARM, even drop the GPU frequency a bit, and you've still got something massively more powerful than the 3DS (and significantly more powerful than Vita). In the unlikely event that they're going with 14nm, then AMD should be more than capable of putting something very competitive together. Plus you obviously get the benefit of using precisely the same GPU architectures between the handheld and home console.
So were Jaguar clusters, but the didn't stop both PS4 and XBO from using eight cores in two clusters (not to mention the many dual-cluster hex-core and octo-core ARM chips).
Edit:
The problem with assuming AMD
aren't providing either of the SoCs is that you have to explain who else is going to launch a gaming console late this year. Here are some of the relevant quotes:
(Link)
(Link)
As far as I see it, there are two possibilities given the above:
1. At least one NX form factor uses an AMD APU
2. Another company is planning to introduce a new console later this year that is both powerful enough to warrant a semi-custom APU and is expected to sell enough to justify the R&D costs involved (i.e. likely 10 million+ units).
Given that the second scenario involves a company developing a console in secret for a year and a half without anyone even getting the slightest hint of it, the logical assumption has to be that AMD is providing an APU for at least one of the NX form-factors.
And this isn't even taking Nintendo's inertia into account, having effectively followed the same GPU team since the N64.