What are disadvantages/Advantages of each. Is it possible to replace an SLA battery with a Lithium battery pack of equivalent capacity?
Lead acid batteries are heavier and larger. Lithium ion batteries are smaller, lighter, more expensive and slightly more hazardous. If the inverter is just an inverter (not an inverter-charger) then the battery type probably does not matter. The only thing to watch out for is whether the inverter has a low-voltage cutoff point. If the low-voltage cutoff point is not suitable for your battery, that could be a problem. Typical 12V inverters are designed to shut off when the battery voltage drops to 10V. That would be OK for 3 lithium ion batteries in series (11.1V battery), but not for 4 lithium ion batteries in series (14.8V battery) unless the batteries have their own low-voltage cutoff.
DO NOT ever charge lithium batteries with a charger designed for SLA batteries. Some inverters have programmable low-voltage cutoff. Some inverter-chargers are so programmable that you can set them up to work OK with Lithium Ion batteries, but you have to know what you are doing. The two most important things are setting the CV voltage to be correct, and disabling the float stage of charging (don't float lithium ion batteries).
If you have a lithium ion battery pack that is rated for 100 Ah, and a lead acid battery with the same rating, the lithium ion battery pack will actually have quite a bit more useful capacity. Lead battery capacity is normally based on discharging to 10V at C/20. If you discharge faster, the capacity will be less. And if you discharge all the way to 10V, your battery capacity will fall very rapidly, and you will be lucky to even get 100 charge/discharge cycles from it without noticeable capacity loss. So in practice, most people plan to discharge their lead batteries only to 50%. So really, when comparing lead acid to lithium ion batteries, you should cut the capacity of the lead acid battery in half. You can subract 10% or 20% from the Lithium ion battery, because you may not want to cycle it to 100% either (but 80% or 90% is very reasonable).
So our 100 Ah lead acid battery is really only good for 50 Ah. And our 100 Ah Lithium ion battery is good for 80 or 90 Ah.
Hope that helps.
with good Panasonic high discharge nca cells, you can get 1000w of capacity for roughly 10 pounds of cells. one good example is 24 cells parallel for 81.6ah and 4 serial for 14.4 nominal. this pack would be about 11 pounds and 96 18650 cells. i have an lfp battery i use with a 1000w inverter its 84ah at 12.8v nominal and only weighs 30 pounds with inverter attached.