Kuja utilizing the power of Trance and souls faces off against the strength and incarnation of might from the Existence born out of the Contact (Fei) into a world of pain and knowing only hate.
On terms of power, Id has a slight advantage. Where Kuja has the major skill and determining factor is his intelligence. I feel Id really lives up to the Freudian term - he is rather basic in mindset and rules more on emotion and forces he doesn't even understand then intellecta nd cunning like Kuja.
If they both encounter each other without previous knowledge of each other and fight Id will take the majority. However if Kuja has knowledge(prep) he can easily subdue Id. Well...not easily but he will. Kuja is cunning and intelligent.