If you're using the analog output of the CDP's then chances are they will sound different. I posted these in other threads but here's a few diagrams of the soundstage of some CDPs (and also DACs, since the only real difference is the transport and SPDIF/USB transmission) I got to try before, plus some text on the tonal qualities. Triangles are vocals, rectangles are guitars, and circles are the drums (including cymbals but I didn't make them distinct; bass drum is large oval).
Fig. I : generally this is what the Marantz CD5004 and NAD C545 soundstage look like - drums go all around the head, bass drum near the vocalist. Sound was a touch too warm for me; drums had impact but sounded too deep, like somebody stuffed pillows inside them all. Other gears used were the Burson Soloist, Meier Cantate.2, and Sennheiser HD600.
Superpro 707 DAC : unnatural drum placement is not this severe, but still a bit too loud over the other instruments and not behind them
Fig. II : This is basically what my Cantate.2 sounds like using its "cheap" USB DAC. Soundstage looks small, but everything in a "proper" location relative to each other. Sound is a bit more balanced but I wouldn't mind a little bit more bottom end and treble extension; most sources tend to go overboard on the bass though.
Rega Apollo : Soundstage close to Fig II but wider, but tonally too warm, dark even.
Arcam CD72 : Similar to Fig II but wider everywhere, but easier to pin point sound sources also; drum hits were more authoritative/punchy but not necessarily that much louder
Cayin CDT-50 : Similar to Fig II but wider by a little bit; pin point sources are better than USB DAC but not as good as Arcam; tonally the midrange and treble (female vocals) are noticeably "sweeter" where the Arcam sounds "dry" by comparison (if I hadn't listened to the Cayin I wouldn't really think of it as dry-sounding)
Cayin CDT-23 : Similar soundstage to CD72 in size, but not as much in terms of pin point accuracy; very powerful "live" sound - difficult to describe but if you listen to "big" or "epic" compositions like classical music, symphonic metal, etc it gives an impression of the performance stage being "huge," like there's a wall of sound (not the same as when Grados are throwing everything on stage at you on symphonic and power metal)
HRT iStreamer : Similar soundstage to USB DAC but a little bigger, not as large as CDT-50; tonally like a lower-cost version of CDT-23 with less pin-point accuracy (but overall great value for money in my book)