The lithium batteries are also no different from deep cycle FLA as far as usable stored power. And they are not as good as deep cycle FLA for voltage retention under load. Those little 10AH batteries, typical with Lithium, are expensive. They cost $150 apiece. They are 10,000 mAh, but you can only use 8,000 mAh (80% DoD) or it will ruin the battery and it will be no good in 50 cycles, just like the one on the toolbox.
Fully charged they are 4.2vpc, or 16.8V. Fully discharged they are 3.2vpc, 12.8V. A drop of 4 volts from fully charged to fully discharged.
A 12V deep cycle FLA fully charged is 12.75V. Fully discharged is 10.8V - a drop of only 2.25 volts.
Any time you power anything electric, especially motors, to get rated power output in watts, as the voltage drops the amps goes up and so does I^2R losses in the motor winding. An inverter is no different. So your motor or inverter is more efficient on FLA as the voltage drops under load than it is with Lithium Polymer because you're dealing with much more voltage drop on lithium than you are on FLA.
You go to 12 cell 24V FLA, fully charged is 25.5V, fully discharged is 21.6V, a drop of 3.9V.
The equivalent lithium is a 6-cell, fully charged is 25.2V, fully discharged is 19.2V, a drop of 6V.
Most 24V inverters, you get down to 22V and you are at the inverter's low voltage cutoff - go any further than that and the inverter becomes so inefficient it creates more heat than it does power output.
So I don't get the love affair with lithium batteries. They are not efficient for charging - they get extremely hot. They are not efficient for discharging - they create so much heat during discharge that the little 10AH batteries shown in my photo are uncomfortably hot to the touch when the aircraft lands. Heat is wasted power, and that's why Tesla batteries have a glycol cooling system in them - they get freaking hot and they are a fire hazard when they get hot.
What I think it boils down to is that people buy into a lot of hype and marketing propaganda because they don't have the technical knowledge to know better.