Fixed biasing gives a bit more gain (all other things, i.e. supply voltage etc, being equal) because the plate-to-cathode voltage is greater. Also, it enables you to get into Class AB1, which is more efficient, and delivers more output power than what you can get with Class A push-pull. You bias the output tubes to get somewhere between about 60% and 85% of the maximum rated dissipation (with 70% being a conventional happy medium). This keeps the tubes from over dissipating under full power, and creates the bias voltage condition necessary for the B-load line to kick in when the driver signal at the control grid gets a big enough swing to create cutoff in each alternate tube.
Cathode biasing is 'automatic biasing' because if the average tube current changes, then the average voltage drop across the cathode resistor changes, and therefore the bias voltage is automatically adjusted. You can run output tubes at 100% of their rated dissipation with cathode biasing (i.e. Class A push-pull) without biasing problems (but you ideally want to double the plate-to-plate reflected load, over what you would adopt for Class AB1, to get maximum power transfer, but even then you still don't get as much power efficiency as Class AB1).