I think both can be true.

A client CPU spends most of its life idling. Thus, the key to good battery life in client computing is, generally, idle power consumption. That means low core power draw at idle, but it also means shutting off peripherals that aren't in use, turning off clock sources for said peripherals, etc.

ARM was built for low-power embedded applications from the start, and thus low-power idle states are integrated into the architecture quite elegantly. x86, on the other hand, has the SMM, which was an afterthought.

AFAICT case for x86 ~ ARM perf equivalence is based on the argument that instruction decode, while empirically less efficient on x86, is such a small portion of a modern, high-performance pipeline that it doesn't matter. This reasoning checks out IMO. But, this effect would only be visible while the CPU is under load.