How much does CD player affect overall sound?

A system is only as good as its weakest link.Each component,the cables,positioning,and the room are all important as is the symmetry of all put together.Linn always felt that the earliest components in the chain were the most important(the table was more important than the arm,which was more important than the cartridge...).If that logic is followed,the CD player or source component is the most important piece in a digital system.I have a half dozen Good CD players and DACs and they all sound different.

While the previous posts are correct, IMO, you can only appreciate quality source components if your downstream gear and speakers are resolving enough to let the better source gear shine. My own experience, in which I upgraded from an entry-level CDP that retailed for $500 to a well-regarded tube CDP that retailed for twice as much, underlined this point. I could not hear a lick of difference between the two CDPs. The more expensive unit went back. Since then, I've upgraded my amp, preamp, and tweaked the system a bit. I am in the process of upgrading speakers now. Once that is done, I will revisit the digital source upgrade.

IMO, your gear is very capable of resolving the differences between CDPs. I would focus on home auditions that allow you to compare your current CDP with others, using familiar discs. If you feel any improvement is worth the added expense, go for it. You can also keep the Cambridge as a transport, and try out stand-alone DACs. Many new models are on the market from well-known manufacturers who have never before offered a separate DAC (Sim Audio, Cary, et. al.) This will give your system some added flexibility for the future. Just remember to use a respectable digital interconnect.

Have fun!

A wise person once told me that preamp, cables, amp or speakers will not PUT BACK what is not there from the start when asked about the importance of a great source.

A lot, but so does everything else. There really is something to system matching. That said, I would have to ask what you feel you are missing that a new CDP would bring to the table.

You’ve got some nice gear, however both the CJ and the B&W’s have a very unique house sound. I have found CJ preamps to be overly dark, and slow (IMHO based upon personal experience with the Premier 3 and the Premier 14). I’ve also found the B&W to be a tab dark for my liking, unless properly matched (based upon poorly executed dealer demo’s).

FWIW, I’d rather have a mediocre CDP with a great pre/amp/speaker combo, than the other way around (a great CDP with a mediocre pre/amp/speaker combo) any day.

Transnova said all and said it well.
Garbage in garbage out!