interconnects vs speaker cables vs power cords - which make the biggest difference?

Factors that tend to increase the criticality of speaker cables:

-- Low speaker impedance.
-- Long cable length.

Factors that tend to increase the criticality of line-level analog interconnect cables:

-- High output impedance of the component driving the cable.
-- Use of unbalanced interconnections.
-- Long cable length.

Factors that tend to increase the criticality of power cords:

-- The component being powered has an unregulated power supply and draws large amounts of current that fluctuate widely. Namely most power amplifiers and integrated amplifiers.
-- The component being powered tends to generate significant amounts of electrical noise, that may couple via the power cord to other components. Namely power amplifiers, integrated amplifiers, and digital sources.
-- AC line voltage at the particular location that is lower than nominal.  ("Nominal" being 120 volts in the USA).

Phono cables and digital interconnect cables involve complex issues that I won’t address in this post, but their criticality will vary widely depending on the specific equipment that is involved.

Regards,
-- Al