With faster transistors, they can have a deeper and wider pipeline with additional multipliers, etc. Significantly more instructions in flight and higher instruction level parallelism (ILP). Along with a higher clock speed. And there is one more feature which would seem natural for such a processor to significantly increase ILP.
Simultaneous multithreading (SMT). Using the past processor wars as a lesson, it's better for Apple to implement SMT instead of competing for the highest core count. And, it's significantly more power efficient to add SMT. My conservative estimate is that we'll see 30% but I feel comfortable they'll get a 50% boost over the A9, especially if SMT is added.
At first this seems overly optimistic but it may not be.
I think they can get higher frequency with the A10 over the A9, esp. since it seems to be the case that the 16FF+ process is more efficient than 14nm LPP. A boost to ~2GHz seems reasonable (+10%) especially as 16FF+ will have had time to mature.
From a ST perf/clock perspective, I think another 10% seems reasonable. If SMT is added, this could lead to 20-30% improved performance in MT loads.
So A9 * 1.10 (frequency boost) * 1.10 (perf/clock boost) ~= 21% ST performance improvement.
Layering SMT on top of that could give a best case of 30% uplift (assuming negligible perf/thread degradation from addition of SMT which I would say is optimistic), leading to 57% more performance in a best-case, blue-sky scenario.