Considering MP was somewhat the heart of the band, I'd say his frustrations counted for a big chunk of that missing piece from FII. I'm not dismiss your opinion, just saying it's purely subjective, and I say that for a very valid and rational reason. I know what kind of music you mainly listen to so it doesn't surprise me that you are such a big fan of FII. With it's lack of "prog flash" and attempted commercial sound (in some aspects), it's just your type of album. Now that's not an insult, simply because you know it's true. However, trying to say it has the same heart and passion as Images and Words or even A Dramatic Turn of Events is just wrong.
I'm very surprised JP said that. Comparing the demos to what actually appeared on the album is not just a few minutes of album time.
There is nothing wrong with saying FII has the same heart as IaW or ADTOE (not saying I'd make that case against IaW, although I wouldn't necessarily disagree with it either as I rank the albums 3 and 4). All of this is subjective, including your thoughts on the matter.
Personally I think ADTOE is their most sterile album, like they felt obligated to continue moving along without MP before even finding a new drummer, although I still like the majority of the album. But I'm not trying to convince anyone else to share that opinion or state that as fact, only pointing out that it's not wrong simply because you disagree with it.
If we're comparing FII demos to final, NM is the same. Peruvian Skies is the same. JLMB is the same. TOT is the same. Hollow Years is the same sans a pre-chorus. Anna Lee is the same sans a final verse. BMS had the instrumental taken out and extended into a new song, but the rest is the same, and the cut section appears basically the same in a new song. LITS is the same except for the small section removed towards the end. YNM is butchered. TAMP is quite different.
Two songs aside, it's trimming, which is a standard and benign contribution from any producer, assuming that it was all the producer's input, and assuming the band didn't fully agree with the changes. MP also wanted a double album with additional songs. But there were also songs written that were left off IaW and Awake, so that was nothing new either. Arguably none of the three albums are exactly as the band would have made without any outside influence, unlike all future albums.