If I had to rate both companies in the different areas, here is how "I" would rate them
Service:
TIE (yes Carnival offers GREAT service...equal to Disney, from your cabin stewards, to servers, barmaids...etc)
Food: Carnival-no contest-most options are included, but they do have a steakhouse..I haven't done Palo or Remy though so I can only speak to their included offerings. Disney does have a great buffet lunch, but I did not enjoy their dinners.
Pools: Disney(Aquaduck is pretty much best "slide" at sea, and their pools are freshwater, Carnival's are salt)
Entertainment: Disney for shows,
Carnival for adult entertainment
Kids Club: Disney
Itineraries/Excursions-
Carnival-larger selection/more ships so makes sense
Rooms:
Tie with an edge to
Disney for decor. Carnival rooms are very spacious as are Disney's.
Bars: Tie- FYI..the Casino bars in Carnival do a very generous pour....Be aware of those MAI TAI's!!
Clubs/Comedy: Carnival
Casino..duh
Carnival
Private Islands: CC-
Disney...though Carnival does have Half Moon Cay, but I haven't visited that yet so cannot comment.