I'm betting there will be a huge perceived speed boost simply because Apple will have full control over the device's stack. I'm sure they'll find ways to better optimize the OS for the hardware.

What I /am/ curious to see is if the CPU options shrink per device - i.e. will there be one A-series SoC for "pro-level" computers and one for "consumer", will there be different clock speeds, etc. We'll have to wait until they announce hardware - I'm assuming at their September/Fall event.

Intel may maintain a performance lead on certain tasks that take advantage of things like AVX, though Apple may be able to make up with more cores. AFAIK ARM has no equivalent to the more advanced vector instruction sets of X64 chips.

I do expect ARM to have an instant heat and battery life advantage. It may be sizable if you combine a more efficient chips with smaller process nodes. I expect a bigger gap here than in raw speed.