The CP4 used SCM (spectral component modeling) - maybe that's presenting part of the difference.

Source: https://www.soundonsound.com/reviews/yamaha-cp1

SCM, or Spectral Component Modelling, is the tone-generation system behind all the sounds in the CP1, and it crops up in other CP models too. As is always the way, getting to the precise details behind these marketing‑oriented acronyms is almost impossible. However, it doesn't appear to be just another PCM‑based sampling system: it's impossible to detect any switching of samples as you vary dynamic level for individual notes, and nor are there any obvious changes in tone quality from one note to the next, right across the pitch range.

SCM also allows adjustment of a few piano‑related parameters such as hammer stiffness and, for the electric pianos at least, striking position. There aren't many, though, compared to the two other established piano modelling systems, Roland's V‑Piano and Modartt's Pianoteq plug‑in. It's exciting to see Yamaha apparently getting to grips with modelling again, after throwing down the gauntlet so many years ago with their VL‑series synths, but the CP1 is absolutely not a tweaker's dream. There's some flexibility, but only a little.

Hello Vasilis:

I think you can get to the sound you are looking for using the master EQ and the tone control. Try rolling off the highs a bit and increase the tone on the tone control. There really isn't much that SCM was doing to the CFX sound in CP4 (which is different than CP1). SCM is really only used on the electric pianos in CP4 (with strike position).

I've played both the CP4 and CP88 a whole lot and I prefer the CFX in CP88 personally. The D/A converters are a bit nicer, and I think they do put out a bit more high end. That could be what you are hearing which is why rolling off the high end might be better. Also, what you are playing it though makes a big difference. I have used the same set of DXR10s on both CP4 and CP88 and I do hear a difference in CP88, but in all the right ways.