When "rating" organ sounds, I think the largest part of the tone os actually the Leslie (or sim). Years ago, I heard a DX7 through a wooden Leslie, and it was spot on. The DX uses sine waves, so it was easy to understand. What was missing was the dynamic percussion allocation, but still great.
My biggest "WTF" moment came when my band was doing an affair in a hotel in Philly. On our break, we wandered around, visiting the other banquet rooms and heard the best organ trio sound ever coming from down the hall. When we looked in the room, it was a CORDOVOX, drummer, and sax ... but he was pumped into a Leslie 122. Both instruments sounded "real" to me, and my bandmates.

So, my point is this: the tone is a 2 part symbiosis - each part compliments the other to produce the sound we have come to know and love as that "Hammond" sound. For what it's worth, my PA4x totally satisfies my need for any "B3ing" I need. Back in the day, I needed the actual beast to do the deeds, but in my small studio, in my quiet apartment, I am very happy with the emulations I get with digital recreations.
SV-1 is my Rhodes
PA4x is my organ
Pianos are abundant in almost everything else I use, but my new favorite is the SX900 played with the keys of the SV1 through midi.