So having watched today's Endurance Run part (VJ-137), I have to say there are some weirdly similar aspects to these two games. Consider this: 
-Both were developed by fairly small companies. 
-Both had unconventional/not very good controls. 
-Both were about a very mysterious murder that was actually told very effectively in the context of the story.
-Both murders involved a cult. 
-Both go OFF THE FUCKING RAILS IN THE FINAL ACT. 
I was actually finally starting to dig on the plot of Deadly Premonition, when...George turned into Akuma Mishima...and Kaysen turned into a giant...version of Kaysen. It can't just be a murder mystery, can it? I was even ready to accept the zombies were a result of the gas seeping into the ground and bringing back the dead, sure, why not? But then...George and the whole thing with Kaysen were just SO ridiculous! Anyone else get deja vu from this?

Dude, don't talk to me about that disappointing train wreck of a game. 
@Undeadpool said:

"Both go OFF THE FUCKING RAILS IN THE FINAL ACT."

I've not played Indigo Prophecy, but the ending did remind me of Bioshock. All the mysteries get tied up at the end, and that's really what you're there for, but then they feel obligated to add in a big muscley boss fight that just barely makes sense story-wise. It's like an abrupt shift from telling a story to playing a game and those two things really rub against each other.
 
Kaysen's first beast form did two things: 1) Made Kaysen look like a fat useless idiot because he kept fallin over n yelling, and 2) Completely undermined the emotional scene of finding Emily as a quivering pile of post-rape trauma.
 
Actually a lot of games do that. FF7 killed off Aeris followed directly by a snowboarding minigame, GTA IV killed off Roman followed by a mission where you have to kill about 500 more people, Gears 2 had Dom get all weepy over his wife followed by *active reload* "Sweet!!"
I read a thing about this a while ago, it's called "ludo-narrative dissonance" where the game and story bump into each other.

The final act of IP was insane, but I dug it. I don't get why everyone acts like it nullified what was great about it.

I think the big difference between Indigo Prophecy and Deadly Premonition, for me, is that Deadly Premonition is unapologetically nuts from the beginning. It doesn't take itself too seriously, and it doesn't mind showing that. Some events are foreshadowed a bit, but when it starts introducing new plot elements, the game just takes it in its stride and so does the player -because- the game does.
 
Indigo Prophecy does start off seriously, and so later plot elements come out of absolutely nowhere. They're not even really foreshadowed. It's like somebody wrote a scipt, then ripped out a mid-late portion, as there is no build up or reason for the insanity. If they'd built it up, it could have worked, but ultimately to me it falls flat as it just seems to decide to go in a totally inexplicable direction. And, given that you play as three characters, you miss important plotpoints (like that one with Lucas) as you aren't with them at the time, which makes it even more "wtf?" but not in a good way. For a game that seemed to take itself seriously, its ending seriously discredited it. 
 
Just a personal opinion, though.

I don't really factor what the actual bosses looked like into the overall story of DP. It's a japanese-ass game and there's certain stuff that you just expect. I loved the ending.

What is this.. Indignant Prophanely? Don't you mean Fahrenheit?
 
In all seriousness, I liked both games, but the ending in Fahrenheit certainly didn't live up to the rest of the game.
The DP ending certainly did.
DP = Crazy japanese ending for a crazy japanese game
Fahrenheit = Funky west game with a bad Matrix-style ending.

Deadly Premonition wins. 
 
In Farenheit the protagonist dies and gets resurrected, comes back with Dragonball Z superpowers, bangs the detective who has been looking for him, and has a super baby.  In Deadly Premonition the crazy guy sees really crazy things happen, and he stays crazy through the ending.  I like that better.

" I think the big difference between Indigo Prophecy and Deadly Premonition, for me, is that Deadly Premonition is unapologetically nuts from the beginning. It doesn't take itself too seriously, and it doesn't mind showing that. Some events are foreshadowed a bit, but when it starts introducing new plot elements, the game just takes it in its stride and so does the player -because- the game does.  Indigo Prophecy does start off seriously, and so later plot elements come out of absolutely nowhere. They're not even really foreshadowed. It's like somebody wrote a scipt, then ripped out a mid-late portion, as there is no build up or reason for the insanity. If they'd built it up, it could have worked, but ultimately to me it falls flat as it just seems to decide to go in a totally inexplicable direction. And, given that you play as three characters, you miss important plotpoints (like that one with Lucas) as you aren't with them at the time, which makes it even more "wtf?" but not in a good way. For a game that seemed to take itself seriously, its ending seriously discredited it.   Just a personal opinion, though. "

I'm not really trying to say one was better than the other (But Deadly Premonition was better than Indigo Prophecy/Fahrenheit), it just seems like both really abruptly went a little crazy. I get that DP was always a little bit crazy, but it was crazy in a very down to Earth Lynchian way, not so much "giant boss battles." I mean I can accept the fact that the seeds made Kaysen immortal and...then later a giant monster, or rather series of giant monsters, but seriously, where did the wall crawler ladies come from?

You forgot to add that both had ridiculously stupid long QTEs near the end of the game that had me cursing a bunch.
DP: Running down(up?) the tower away from frog Kaysen
IP: Fighting The Oracle on that rooftop, then running away from police helicopters.

"where did the wall crawler ladies come from? "