you need to listen to both speakers again. Bring cds that you are familiar with. Listen to cymbals, sibilance of vocals, vocals, attack of drums, bass transients. Listen to large symphonic pieces for definition of instruments and dynamics.
The CM7 requires more power than the 683 due to its relatively low sensitivity, so if you have settled on an amp, make sure it can run the CM7 at the levels you desire. If not, than your decision is already made.
I think the 600 series has better center channels than the CM series if you are not planning a perfect match for L,C,R.
I think the CM7 looks better cosmetically.
With that said, i think your focus is too narrow on speakers. It would be better if you branch out and listen to other speakers. For all you know, you cannot choose between the two because they both sound equally as terrible compared to a mystery speaker that you have no auditioned yet. Perhaps, you haven't found your 'cup of tea' yet.