So if 10ah is 10ah like i have read many times then a lithium should not run longer per charge correct? I read others say a lithium lasts so much longer per charge. Whats the actual reality?
If both batteries are the same amp hour, then the voltage drop becomes the determining factor. Lets say that your device has a low voltage cut off at 11.5 volts.
A lead acid (SLA) battery at 11.5 volts is 80% discharged. That means out of the available 10 amps, you have only used 8 of those amps before the voltage drops too low to correctly power your device.
As stated earlier a lithium battery will maintain a higher voltage for almost the entire capacity, in this case 10 amps. Let's assume you can get 9.5 amps from the litium before the voltage cutoff is reached. That is still a 1.5 amp advantage for the lithium.
Stated another way, if you get 8 hours usege from a 10 amp hr SLA lead battery, one could expect 9.5 hours useage from a 10 amp hr Lithium battery.