Your post is right up my alley. I am a classically trained pianist and organist. To play the great compositions for the "King of Instruments" requires a solid grounding in the piano. The great organists, like Virgil Fox, were adamant about constant piano practice. At my home, I usually work on Bach and Liszt pieces (or perhaps some Mozowski studies) on the piano. I have a three manual (that is, three keyboard) Allen digital organ (usually installed at churches) in my home. It is a real blessing to have both at my disposal. When faced with a difficult passage in an organ piece, I practice it on the piano (without pedal)--this forces me to really develop good technique.
I love the piano which is why I visit this forum. But, in many instances, there is nothing like playing a great pipe organ. The accumulation of centuries of knowledge that goes into the art and science of organ building is amazing. I have an incredible tonal spread on my Allen organ. The large 32' pedal stop has a pitch at approximately 8 cycles/second, and the high-pitched stop has a pitch at thousands of cycles/second! The overtones (both harmonic and inharmonic) form incredibly rich and complex sounds. In my instrument, I can even change the temperment so that I can play earlier music in a pitch closer to what hearers centuries ago heard! It is a real experience to play in some keys that are more truly "in tune" (as you probably know, our current "equal-tempered" scale is a compromised system which allows us to play numerous keys on one keyboard).
Unfortunately, many of my pianist friends have been exposed to poor organs, poor organists or both. But when a virtuoso gets hold of a great instrument, it is an amazing experience. My pianist friends are really enthusiastic about Bach, Vierne, Franck and others as it can be played on a great sounding organ!
The literature of the piano and organ are unlike any other instruments. We are truly fortunate as players. Check out the website virgilfoxlegacy.com. Click on the the "chronology" section and view the video clips and you will see some amazing playing (Fox played from memory the most monumental music). Purchase his cd "The Bach Gamut" and the one in which he plays the famous Wanamaker organ.
A while ago I played the large pipe organ (over 15,000 pipes) at the Crystal Cathedral in Southern California at a recital. It was the highlight of my musical life!