Ok so since you (Foro) keep going on about The Fugitive and how many changes there are in it, I decided to go back and have a listen because, just like The Flash, I don't recall The Fugitive being that interesting. So I went back and broke it down and here's what I got:
0-0:48: Intro (short bridge at 0:28 linking the multiple reiterations of the intro theme)
0:48-0:58 Bridge to verse
0:58-1:44 Verse (same chord progression as bridge to verse, sounds like about 6 different chords))
1:44-2:04 Chorus
2:04-2:26 Verse
2:26-2:46 Chorus
2:46-3:08 Solo
3:08-3:30 Bridge (same as intro just different orchestration, less drums)
3:30-3:38 Short bridge identical to bridge in intro
3:38-3:50 Lick (?)
3:50-3:58 Solo
3:58-4:20 Verse
4:20-4:40 Chorus
4:40-4:54 Outro (same as intro)
All told it sounds like there are about 4 distinct different elements (intro, bridge to verse (remember verse is the same melody and chord progression as this bridge), chorus, lick), everything else is a variation of one of these (while orchestration can make a big difference in how something sounds, if its the same chord progression and melody, it really doesn't count as something new and distinct) or a solo.
For comparison I went to Starblind, which was a whole other story primarily because its so difficult to actually hear whats going on with the individual guitars in the background. But here's my rough estimate of the various sections:
0-0:24 Intro
0:24-0:50 Verse (same chord progression as intro, vocal has similar melody to principal guitar)
0:50-1:04 Bridge
1:04-1:48 Verse (less acoustic orchestration but same as first verse)
1:48-2:10 Chorus 1 (guitar licks in the background ala Out of the Shadows)
2:10-2:32 Chorus 2 (guitar licks)
2:32-2:54 Solo
2:54-3:16 Verse (guitar licks)
3:16-3:38 Chorus 1 (guitar lick overhead throughout)
3:38-4:05 Chorus 2 (guitar licks)
4:05-4:15 Bridge to solo (same as first bridge)
4:15-4:43 Solo
4:43-4:53 Solo
4:53-5:04 Solo
5:04-5:46 Riff
5:46-6:10 Into progression with guitar lick over
6:10-6:32 Verse (guitar licks)
6:32-6:53 Chorus 1
6:53-7:48 Chorus 2 twice (guitar licks)
Here there are 5 distinctly different elements (intro (verse is the same as intro), bridge, chorus 1 (Starblind with sun etc), chorus 2 (whatever God you know etc), riff at 5:04). There may be some debate over chorus 1 and 2 but to my ears these are 2 separate melodies that both happen to be repeated in the same format throughout the song. So in terms of distinct different melodic and chord progression elements, Starblind does have more (but only one more). In terms of actual sections (so, changes) there are 14 in The Fugitive and 19 in Starblind. So yes there are more changes in Starblind as well. I think a contributing factor to The flash perceiving Starblind as a lot more varied than The Fugitive when it actually isn't melodically speaking, is that those bits that are frequently repeated vary in guitar lick happening on top of the vocals. So for example Chorus 1 from 3:16-3:38 has a very different lick than Chorus 1 from 6:32-6:53, and it is also a more extensive embellishment. Either way, yes Starblind has more changes, yes it has more different melodic elements, and honestly, listening to both over and over...Starblind just has more going on in it.
Feel free to critique and have input on my subdivisions of each song, but I think in terms of overall melodies and chord progressions (I'm not that bothered about solo's) its fairly accurate. To reiterate: Starblind is in fact, more complex melodically than The Fugitive (not by much, but still).
But just like Foro said, I'm not saying which is better. This is simply breaking both down to get the facts straight.