I just went through a year long hunt for a new CD player that ended with me buying a Naim CD5i. My budget was $2500, but I would have stretched to $3K if something was head and shoulders above the rest in my system.
I listened to the CD5i vs the CD5X with a FlatCap2. That was a $1700 player vs a $5000 combo. I didn't listen to the 5X any without the external power supply. With reference recordings, the CD5X is clearly the better player. It has the ability to resolve a ton of detail without distracting from the drive of the music. Sterophile did a review of this player last year comparing it to the Arcam CD33. I've spent plenty of time with the CD33 and the 5X has that same level of detail, but with a lot more drive and musicality to my ears.
The CD5i is a slightly different animal. With reference material, it sounds great, but it doesn't resolve the same amount of detail as the 5X or the CD33. It doesn't soundstage quite as impressively either. It has a very musical and involving presentation, though, which I'd describe as fun and lively.
Where things got interesting was listening to non reference recordings. As you'd expect, something like the Tord Gustavsen Trio sounds fantastic on just about any respectable rig. However, I listen to a ton of metal and hard rock. I love my jazz and classical, but the heavy stuff still dominates about 70% of my listening time. The CD5i managed to inject life into just about every CD I threw into it. With marginally recorded music, the 5i still had me tapping my toes while the 5x had me paying attention to the warts in the recordings. It can be a subtle thing, but it was a surprising distraction. I ended up buying the 5i because I felt that it was the best compromise of sound quality across the range of music that I listen to on my system.
What's the moral to this story? Audition a wide variety of CD players, preferably in your system, and trust your ears with your music.