My experience wih cove or strip lighting is that for a given illumination level the wattage consumed per foot comes out the same no matter what the voltage. The strip lighting designers will adjust things to give same lumens per foot regardless of supply voltage.
However you are correct, a 24V system will have half as much current as the 12V system. Consequently the losses in the wiring will be a lot less with the 24V system.
If you are running the cove lights from a battery. You should get longer run time with 24V before battery is depleted.
Unfortunately another wrinkle is the battery capacity also comes into play. You need to double up on 12V batteries to get 24V. Since batteries only come in certain sizes you my end up with an amp hour ratting differeent from wht you exxpected. When series wiring 12V batteries to get 24V the amp hour capacity is the same while the voltage doubles.
Parallel wiring the batterieis doubles the mp hour capacity but keeps the voltage the same.
What may be a considerattion is how you are going to develop that 24V source. 24V chargers may be less common or available in your area or be quite a bit more expensive.
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