I've flown them both in C and F in the past year (though not SQ's new seats). IMHO, they're the world's two best airlines, so I agree with others that the differences are minor in most respects, at least in C (which is what I fly much more often). In C I'd say they're about equally great. In F I'd give a definite edge to SQ because I like the seats better. I'd give a definite edge to CX's HKG lounges over those of SQ in SIN.

Interesting posts at the SQ forum and other websites re SQ's new seats. C seems to be a smashing success, F seems to not be going over so well.