AMS make some interesting stuff but they're most notable for their up to 1 watt NFC booster ICs with inbuilt antenna auto tuning.
What this effectively means is that you can make your coil pretty much however you want it and the AS3923 will compensate an insane amount for a poor antenna design/implementation.
Now I gather from your post that you got to the sub-heading. I'd like to point out that 'mobile payments' are a use of NFC technology, not a hardware type so much.
So really, bearing that in mind, the differences in NFC implementation between iphone 6 and lets say a GS4 are:
Power output (Booster IC)
User space access
AFAIK they will both do payments (anyone care to comment on that? I've never tried).
IF the Apple would let you touch it's precious NFC unit with a third party app then I really can't see any reason why it would not work with a passive device like the NFC Ring.
It's not a problem with the protocols because they're based on the NFC standard.
It shouldn't be a power issue because of that IC which should compensate for the antenna and bring the power output up to an appropriate level.
It shouldn't be a problem with the size of the NFC antenna because as long as it produces a strong enough RF field then there will be interaction with a passive device.
Pretty much the only thing I can see that is stopping use with passive tags is the lack of access to the hardware from user space.
That's not to say it's a definite, but I can't see why it should be impossible.