It's supposed to, but current reports indicate that battery life is the same or worse with this lineup (maybe the overheating situation is to blame)

That’s great as long as the software doesn’t change to fill the new performance headroom. Unfortunately, software seems to follow the same law as bureaucracy: expand until all available resources are consumed.

It seems that in this case the performance per watt is essentially the same. There is no point in rushing to sleep if perf per watt is constant, you will only end up giving the chip a higher amperage and loosing even more to heat in the power delivery (internal battery resistance, traces and power supply). The slower cooler phone will perform as well and also deliver better sustained performance over time as the peak burst current of the battery decreases.