1. All too often published specifications are just another form of marketing, particularly when they're published via press release. Which is to say they're fiction, or at least heavily qualified facts.
2. It's possible one bike is more aerodynamic. The human-powered land speed record is 82 mph on flat ground; a top cyclist can usually put out about 500-600 watts of mechanical effort for a minute or so. The LSR was done on a very specialized
aerodynamic recumbent bike.
The capacity of the battery is only a factor if the total battery power output limits the motor's power output. For example, the 2004-2009 Toyota Prius has a 1.3 kWh NiMH battery rated for a 20C discharge (20 * 1.3 kW = 26 kW). The MG2 motor is rated at 50 kW, but because of the small battery size
in combination with the 20C discharge limitation, the motor's actual output is limited to about 25 kW.
The C-rating for a battery is a measure of how quickly the battery can charge or discharge. A 1C discharge is the discharge rate (power) at which the battery will be completely depleted in 1.0 hours; a 10C discharge is the power at which the battery will be completely discharged in 0.1 hours (ex 10 times the capacity of the battery).
Ex for 1.3 kWh battery:
1C discharge is 1.3 kW, the battery can supply 1.3 kW for 1.0 hours
10C discharge is 13 kW, the battery can supply 13 kW for 0.1 hours
20C discharge is 26 kW, the battery can supply 26 kW for 0.05 hours (3 minutes)
This is a pretty simplified explanation, and that's good enough for hand-waving : P The Audi e-bike battery can fully power the motor if it can discharge at > 4C, which seems pretty reasonable. That leaves either the less powerful bike's top speed claim being a fabrication or else it's extremely aerodynamic.