In the labyrinth of eternity
No Prayer is easily in my top 16 favorite Iron Maiden albums.
To Perun's point about "back to roots"--this is exactly what Maiden were saying at the time. They were hugely inspired (intimidated) by Guns n Roses' success. They had no interest in speeding up further than they already did on the 7th Tour of a 7th Tour to compete with thrash, speed and death metal that had been gaining in popularity but were still leagues behind in stature and sales, so that wasn't an option.
The path they took was to try and compete with the likes of GnR, Poison, etc. A little more sleazy (Bring Your Daughter...) a little more tongue in cheek (Public Enema...)--at least in song titles. They likely thought they could blow these guys out of the water because of their skill as songwriters, playing chops and live show. It wasn't truly simplified (that would likely be impossible given the band's skill and compositional tendencies), but it was a purposeful return to the earlier, simpler times. The repetitive epics were gone, Bruce changed his singing style and Adrian freaking left the band, citing his disagreement with this "stripped down" approach.
Maybe that line was all just bollocks and Rod's way of justifying the greatly reduced size (cost) of the stage show, but it was clear at the time--from the album cover to the stage set to the shorter songs--that they were feeling nostalgic for the past when sales (of tickets and albums) kept increasing every year. At the time, I could see the merit in taking this approach. The problem was that it seemed forced, reactionary to the scene around them (rather than doing their own thing and leading the genre) and I didn't like any of the songs.
(I was writing this while Nuno's post came in--great minds think alike!)
I know that this is what they said and were aiming for at the time. My point is that it's not what they ended up doing. NPFTD is a far more natural progression in terms of songwriting than people tend to think, and I have the feeling that it's the stripped-down image Maiden were sporting at the time rather than an actual appraisal of the music that leads to this view. And with that 'image', I also mean the sound and production of the album. It's simply not supported by the songwriting.