Incremental encoders output a basic Quadrature (A/B usually along with a Z index) signal, which is counted by the drive (aka the drives internal encoder counter increments). When everything powers on, the drive has no idea what the motors rotor position is, or whether it has moved.

Absolute encoders output their rotational position, via serial communication.
Some setups it'll be a once per revolution repeating output, whereas some can keep track of the position over multiple turns, so even if the drives/motors lose position/power, it is theoretically possible to not need to rehome to regain position.

In terms of which is best, for simpler controllers, there's not really any difference.
Both types of drives usually accept some form of step input (be that Step/Dir, Quadrature, or CW/CCW), output a generated quadrature signal should you want to feedback position to a suitable controller, and all the usual inputs/outputs will be fairly similar.

AXBB outputs fairly common Step/Dir, which the majority of servo drives will accept.
The only thing you might need to do, is enable virtual gearing within the drive, so you don't need quite as fast a step signal.
I'm too tired to do the calcs just now, but some of these drives now have a ridicousuly high step count per revolution, so with the AXBB which is capable of 400KHz, you might find the 400KHz step rate is the limiting speed factor, and not the servo speed. So by using the drives internal gearing, the drive will move more than one encoder count per received step.