Or in the water analogy world, which is better, a pair of 5 gallon buckets OR a 10 gallon bucket. Same capacity, different form.
The big advantage of 24v over 12v is in your wire and SCC sizes. For rough napkin math a 3000w inverter ÷ 12v = 250a of current which needs 3/0 honkin welding cable to connect. However, 3000w ÷ 24v = 125a which is only 4awg or so. Much smaller wire, much smaller fuse, easier to handle for crimping and fishing.
The other place the 24v is better is your charge controller. Since charge controllers are rated by OUTPUT amps, a 40a SCC can do 40a × 15v = 600w of panels, but the same controller at 24v does 40a × 30v = 1200w of solar on the same unit.
When you're looking at amp hour ratings, that's how many hours you can draw 1 amp, but what's important is watts (amps × volts = watts × hours = watt-hours) and that's your loads. So, say you want to run your MargaritaMaster 3000 for a party (that you'd better invite us to!) and it needs 240 watts to run. On a 12v system that would be 240w ÷ 12v = 20a. So, if you made margaritas for an hour that would be 20 amp-hours. Now, say you had a 24v system and made margaritas. Now it's 240w ÷ 24v = 10a, or 10 amp-hours for an hour of margarita making. Either way, you're still using 240 watt-hours. And by now you're probably a bit tipsy.
Does that help make sense?
About the only place amp-hours comes into play is when you're going from lead acid flavors to lithium. In general a lead acid battery can only be drained to 50% of it's rating before you start hurting it, so when you look at that cheap WallyWorld 100ah battery, you can only really USE about 50ah of it, which meand if you replaced it with a 50ah lithium you'd get the same Usable Energy out of it. With the cost of lithium coming down and the fact that you need twice as many amp-hours of lead to get the same usable watts, lithium is pretty much the answer outside of specific use cases like long periods of sub-freezing temps.
