Choosing a cabin is a more science than you might think. While I would not make a blanket statement about all cabins on deck six, you should be aware of what is above you and below you.
Above you are more cabins - that is good. Below you are public spaces. Some public spaces (like the library) and quite - that is good. Some public spaces (like the disco) are very noisy. That is okay if you are in the disco. That is not so good if you are in the cabin above the disco and you are trying to sleep. That said, I would say more than 50 percent of the cabins on deck six have the potential for being noisy.
You don't have to upgrade all the way to deck nine. All of the deck seven cabins are good since all have cabins above and below.
Deck nine is okay if you stay forward of the elevators. However, being that far forward means your cabin will pitch (up and down movement) more than a cabin near the middle of the ship will. Also, the higher you go the more you will feel the roll (side to side movement) of the ship. That said, it has been my experience that if the ship is rocking, the entire ship is rocking.
While I have not been on the Conquest, I have been on two of its sisters (the Glory and the Freedom). The Conquest, Valor, Glory, Liberty and Freedom are all the same except for the interior color scheme and the room names (the layout is the same). On the Glory I was in a rear facing balcony cabin on deck seven. On the Freedom I was in a side facing balcony cabin on deck nine (9253). Here are some pictures.
Some of the pictures are claiming to have been moved. They have not been. I don't know what is wrong. All the pictures are showing properly in my review -
http://www.cruise-addicts.com/forums/f6/review-carnival-freedom-june-12-18-2011-a-171229/ (go to Sunday, June 12 for the cabin photos) ...
Cabin 9253 ...
A view of the port side balconies ...
A view along the port side ...
A view along the starboard side of the Glory ...