1. Battery runtime is mostly dependent on the discharged current.
2. As battery is drained then the battery voltage decreases.
If you use a simple discharge method using a resistor then towards then end the voltage drops and so does the discharge current.
Whereas using constant power throughout the test the power is kept constant and runtime is more representative. This is because most loads are not resistive and required constant power.
You can also read my some of my contributions:
Conference Paper Battery Capacity and Discharge Current Relationship for Lead...
Thesis Discrete linear constrained multivariate optimization for po...
Furthermore, practically one can program a sequence of constant power discharge phases to mimick electronic loads - for instance in my work with biofuel cells I can set the potentiostat to mimick a BLE device startup/handshake/transmit/shutdown sequence.