I have travelled both airlines, and I can tell you that Singapore Airlines is much better. Last time I travelled in CX was in economy, LHR-HKG, and the seats were a bit cramped, so I can not tell you about their First and business class, but I presume their are good. I have travelled in all classes in SQ, so, I would say SQ Economy Class is much better thatn CX one. Business Class is great, and First even better. The service is marvellous and seat, I don´t have words to describe how confortable they are.
BTW, I´ll be flying in SQ, next month on 8th of June, LHR-SIN-JKT, and then in the beginning of July, JKT-SIN-MEL, and finally in August, MEL-SIN-LHR.