Yep, a good battery makes a lot of difference.
The charging system generally provides around 13.6 volts, but if the battery is low (or old), it will be reduced trying to charge the battery.
Reduced voltage plays havoc with the ECU. The stock ECU does not compensate for reduced voltage, and as a result, the fuel injectors are not opened for the correct time, and the ignition is not providing nearly the same output - very important at start upand higher rpm. If voltage is too low, the fuel pump cannot provide the required volume for high rpm use, and the engine runs lean.
Battery voltage below 12.6 is for all intents, considered dead. Fully charged, a good battery will show 13.15v after it is charged and allowed to stabilize for 20-30 minutes. Older batteries should charge to a minimum of 13.10v. Even then, if it does not hold a load (like starting), it will not work correctly.
I have watched some guys fight tuning a bike on a dyno with a low battery. Hours of work later, and the tune is completely screwy and rich when the battery is fully charged. Unpluggng the light connectors (front and rear) can help a lot.
A good trickle charger can extend the life of a battery by several years, and can help when dyno-tuning. however, most of these devices can cost as much as a battery. If anyone is interested, I can show you how to build a very good trickle charger for little to nothing. A good cell phone charger (for an old phone), a cheap resistor, and a couple of connectors and you are in business. Even a wiring neophite can build this.
-WT