Hi,
Simple answer: There is no simple answer for your question.
The only thing that is very likely: the less voltage you give to the MCU, the less power it will draw. Thus - just from the view of power consumption - supplying the MCU with 1.8V is preferable.
It depends on many things.
* power consumption of your load and behaviour with respect to time
(It's not inly the MCU tgat draws current, usually there are other components, too. The application may have some states of power consumption: deep sleep, idle, active power ... and you need to know peak current to correctly choose your regulator)
* battery behaviour. Is the 4.35V only during charging? Are you interested in high efficiency even in charging mode? In either case you need to know peak expectable voltage (even for a short pulse during charging)
i know LDO generally very inefficient.
"Generally" this is not true.
* in times of low current consumptions they often are better than switching regulators.
* when V_in - V_out is low they often are better than switching regulators.
Both may be true or not for your application.
But for sure if you have an appllication that continously draws 5W@2.5V .... and the supply voltage 24V .... this calls for a switching regulator.
Many (all?) voltage regulator manufacturers and distributors provide interactive selection tables to choose the best regulator.
They are free to use.
But the values are for steady state only, thus you can do only a preselection. For a detailed selection you need to read datasheets and compare them (maybe with the use of EXCEL) according your
dynamic load conditions.
Klaus