I've had 3 different CDP's in my system over the last few years and all of them gave a different presentation with instrument seperation and staging.
I had a CDS3 and XPS2 which gave a very flat soundstage narrow stage with okay instrument separation. When i got it i bought it off a chap using Shahinian Obelisk and the Naim sounded good with those speakers so so good with mine though.
I had a MF Nu-Vista 3DCD which gave a very wide (touching the walls wide!), deep (in my lap to back wall) and instrument seperation was first class, but after living with it for some years the lack of bass just made it a bit thin sounding. If it had the bass weight of the Naim i would still have it, it went sometime back as the prices were reasonable.
And lastly my PS1, which i'm now on my second one and is my main CDP at the moment. This give a a good stage, not as wide as the MF and not flat like the Naim but it okay. Instrument separation is mediocre but can be bettered with mod's but i'm not bothered by it at all. To be honest it's not the best CDP out there but everytime i spin a disc it puts a smile on my face unlike the two above, probably down to the cost of it!
So it could be the disc spinner or it could be a combination of boxes in your system, the only way of finding what you want is to do some demoing.