The advantage is greatly improved travel distance, with a big weight, handling, and wallet penalty.
With 24V, 100aH of LiFePo4, you're looking at a 55ish pounds of batteries, and expect to pay around $2000 for the batteries alone, probably more. If you go SLA, well I think that might exceed 150 pounds.
I'm no expert on these things, but from what I've read around here, I gather:
For your battery and motor combination to squeeze the maximum number of charges & discharges you can out of the batteries life, choose one where its 1C rating coincides with however many amps your motor will draw continuously at full throttle and at cruise speed.
36V 20aH batteries paired with hub motors sold in the 500W flavor is popular because this combination approximates that.
The inexpensive 20aH LiFePo4 duct tape batteries allegedly have been tested to last for 1000+ charges, but that testing was at a steady current draw of 20 amps, or the 1C rating. A typical hub motor at 36V should put your discharge rate pretty close to 20amps. A battery with much less capacity, say 10aH, or much more capacity, like in your 100aH example, takes you out of the best-bang-for-buck zone you could get by matching the 1C rating to the continuous discharge rate.