Dear Monk, I trusted you when you said the notes were the same, it still bakes my Noodle though!
Nice example above with the Cmaj7 to C#dim7, Dm7 to D#dim7. Just like Aint Misbehavin, one of my favourite songs ever. The Em7 doesn't seem to fit as well, but I am probably just hearing Aint Misbehavin', or playing a bad inversion. I Normally play it as C, C#dim, Dm7, G7. So let me see:
Gdom7 = G, B, D, F
D#Dim7 = F#, C, D#, A.
Um
, I wasn't expecting that! I was expecting them to share lots of notes, because either sounds really good as the fourth chord!