Good question. I have a CP-35 and an Adcom GFP 750 on my living room table right now, and trying to answer the same question.
I find that the Classe sounds a little "smoother" and "warmer", but less revealing, especially in the high end.
The "passive" mode on the Adcom is amazing; I feel like a veil is lifted when I enable it. On the other hand, it can be bright and a bit less "involving" (oh, that's a subjective word!) than the Classe.
I find the Adcom sounds better on very well-produced music and on Jazz, where accuracy is really appreciated (Dire Straits, Lyle Lovett, Miles Davis), and that the Classe sounds better on rock (Pink Floyd, U-2), where warmth and coherence are important.
It's worth noting that I am using these with equipment of lower quality than they would normally be paired with (Rotel RB-981, which is a bit sloshy), and a Yamaha single-play CD player that may be a bit on the bright side itself.
Tough choice, depends on your taste in music and in sound.