The Amp Hour rating of a battery tells you how many amps a battery will deliver and for how long.
So a 15Ah battery will deliver 15A for one hour, or 7A for two hours etc. - not that useful really.
To get the Watt Hour rating multiply the voltage by the Ah rating.
So a 36v 15Ah battery is 540Wh - a 48v 15AH battery is 720Wh, a significant difference.
Riders use between 10-20Wh per mile depending on fitness level, terrain, wind, weight etc. One member here (who live on the French/Spanish border, so is very fit) reckons he's got it down to 7Wh per mile.
Obviously a 48v battery will be heavier than a 36v of the same Ah rating, as there are more cells in it.
Do be aware that you cannot just put a 48v battery onto an existing 36v system. Although motors can take overvolting there are capacitors in the controller that probably can only take the rated voltage, so it (and it's display) would need to be changed.
Cost to charge is 2-3 units of electricity - depends on your tarrif
Never seen capcity to weight ratio's - Dude, batteries are heavy - end of!