Hi tugboattam, there is a difference in the measurement of amp hour capacity between Lead acid and Nicads / Nimh batteries.
The Nimh cells are rated for their capacity at the 5 hour (discharge) rate but lead acid batteries are rated at the 20 hour rate.
For a 4 amp hour lead acid battery, then 4 amp hours divided by 20 = 0.2 (amps) will give the full capacity of the battery for 20 hours. If the current discharge rate is higher then the efficiency of the battery goes down and there is less current available. Typically some of the power in the battery comes out as heat, so warming up the battery.
For the same rated Nimh battery then 4 (Ah) divided by 5 (hourly rate) = 0.8 (amps, or 800 mamps) discharge for 5 hours will give the full discharge of the battery as per rated capacity.
Any discharge current higher than this (which we all do) will decrease the efficiency of the battery, heat etc.
So as has been pointed out previously the lead acid battery will last a lot less than the Nimh battery depending on discharge rate in amps.
C is often used as a reference to capacity of the battery. The charging rate is usually recommended as c divided by 10 ( so if C = 4 amp hours then the charging rate is 0.4 amps, for 14 hours). The extra 4 hours is that the losses in the charging are taken into account by an extra 40% charging.
Also you may see a recommended maximum discharge rate of 10C for the 4 amp hour battery this 10 x 4 =40 amps. Only if it says so!!
Lead acid batteries have a recommended charger and these do not apply a constant current ,but a constant voltage, with some current limitation. This is called taper charging as the the charge rate (current) tapers off until fully charge is reached. The voltage on the battery rises as the charge goes on until it nearly matches the charging voltage.
Nimh cells have constant current charging.
I personally break all of the above rules but if you break the rules it best to know which ones they are!
I agree with previous contributor and throttling back is best bet, but a bit of extra power for stopping is most welcome.
My (defunct) L/Acid batteries are mainly used to hold down things being glued and this is where weight is good!
Hope this helps,
regards Roy