Well, in regards to the first question generally a processor's performance is proportional to the sqaure root of it's area at a given frequency and voltage, and it's active power use and leakage are both proportional to it's area. So yes, a smaller core will be able to accomplish the same task for less energy even though it takes longer.
Now it used to be that processors power budget was dominated by active power and the solution was to scale clockspeeds and voltage levels. As we move to smaller process nodes it's more about leakage power, which only goes away when you power down the core meaning that now race to idle is a better choice. But that's tangential to the bigger/smaller core issue.
Now it used to be that processors power budget was dominated by active power and the solution was to scale clockspeeds and voltage levels. As we move to smaller process nodes it's more about leakage power, which only goes away when you power down the core meaning that now race to idle is a better choice. But that's tangential to the bigger/smaller core issue.