Filter capacitance-how does it relate to amplifier performance?

I have a Unison Research Due amplifier that drives my Totem Forest Signature with ease. It has 100wpc in 8ohm and 180wpc in 4ohm. It has a filter capacitance of 80,000uF

I previously had a Atoll in100 amplifier 100wpc in 8 ohm, 140wpc in 4 ohm Capacitance of 31,474 uFMoving up the Atoll line the in200 has 120wpc in 8 ohm and 200wpc in 4 ohm and filter capacitance of 62,000uF
The Atoll in300 has 150wpc in 8 ohm and 260 Epcot in 4 ohm with a filter capacitance of 81,600uF. These also had no trouble driving my speakers.

My understanding of capacitors is that they store energy. Does this mean that my Due amplifier is just as powerful  as the on paper more powerful Atoll in300?

For comparison sake with my Due amplifier I demoed a Plinius Hautonga integrated amp with 200wpc in 8 ohm and 280wpc in 4 ohm. I did not hear any appreciable difference in bass or other frequencies.

So 3 questions.

1) Is my Due amplifier much more powerful than the wpc  indicates?
2) How does filter capacitance relate to power in an amplifier?

3) Why do manufacturers rarely publish this spec? I could only find a few examples.

Thanks