You'd need some awesome API design for making up for that hardware difference
What I don't agree with is the many fanboys postulating that D3D12 is going to bring similarly large performance benefits to Xbox One, which is something I see all-over places where armchair developers congregate. It'll be positive for many reasons, some of them (smaller) performance reasons, even -- but D3D12 won't be the end of PS4's performance advantage.
They're not that far apart if you ignore those pesky 4 extra graphics clusters that are reserved for compute (and also the fact that if you're rendering pipeline needs/can use compute up front (IIRC, some renderers do this to compute lighting in deferred rendering) then they're still being used.
Otherwise its 12 clusters at 850Mz vs 14 clusters at 800Mz. Overall, the difference is less than 10% (again, ignoring the other 4 compute clusters, which is a rosey view). Its not so much the shader throughput that's holding Xbox One back, as much as it is poor utilization of the ESRAM. Honestly, though, when MS found out they were going to come up short, they probably should have enabled the extra two backup clusters and taken the hit on yield early on, and re-reved the silicon to add two more to keep yields up -- doing so would have closed the gap and then some, but they might've looked at that and decided it would be bottlenecked by other resources, or was impossible by design. It also might have been too hard on yield, because you'd need completely flawless chips since the ESRAM doesn't have any redundancy/mitigation in its design at all. The PS4 chip also has two extra clusters, but it'd also put Sony in the same boat of needing flawless chips and would hurt their yields similarly, which they wouldn't have felt pressure to do.
I think Sony came out with the better architecture this round, they actually have slightly-lower total memory bandwidth, but putting it to use well doesn't require careful management like the Xbox One does. If a game does use the ESRAM well, it'll actually have more bandwidth available than PS4, but we're talking about achieving near-peak efficiency. Had the Xbox One had GDDR5 *and* ESRAM, that might have been something fancy.
Next Gen, we'll all be on HBM or similar with greater than 1TB/s bandwidth, 2TB/s probably.