The 'Fuji-colors' are mostly a product of the JPEG-engine in the cameras. While there is a slight difference between the 16MP and the 24MP, most differences are due to the JPEG engine and between lenses. Some of the older lenses (the fast 23, 35 and 56) have a 'special' film-like quality. It has mostly to do with how they render color and contrast. Using these lenses on the newer cameras, results in the same effect. Fuji-purists sometimes praise the older 16MP sensor for its character, but to my eye the 24MP sensor is just as good and has the resolution to do additional cropping. I've owned 6 Fuji cameras over the past 9 years (and still own 2) and the newer cams are just as good as the older ones (if not better).
I've had the XP1 but upgrading to the XP2 didn't affect the colors in RAW. In fact, the JPEG-engine in the newer cams (like the XP2 and the XE3) can also control the film grain and has a few more film simulations that can be an advantage. Esp. Classic Chrome can be made to look similar to the 'Leica-look' (I've used a/o the M8 and the M262).
To learn more check out fujiweekly.com and the film recipes outlined there. Also check-out the RAW and JPEG manuals of Thomas Fitzgerald. He gives very good advise on how to set sharpening and noise reduction. Fuji's JPEG engines are too aggressive to my liking, so I dial down NR to -2 or -3 on the 24MP-cameras and Sharpening to -1 or -2. I use Capture One as imo it works way better with RAF-files than LR.
PS. with the new XP3 out, second-hand prices for the XP2 dropped. While not as low-priced as a used XE3, an XP2 is now great value-for-money.