You really have to consider all major stages of the operation of the player, this is why you often get better performance out of separates rather than throwing all you hope into one integrated CD player.
The transport
The digital conversion
The output stage
(Even possibly input stage if it functions as a DAC)
Each stage should be carefully considered by any audiophile and maximized to taste. This is after all a game of preferences. But I do firmly believe that each piece is important starting from the very first watt and that nothing can be retrieved if it is lost further up the chain.
Sam