To start off, I honestly feel I never should have got DR2 and gotten this one instead. If you have a choice between the 2, get this one. It released at a lower price, contains an additional zone, has better/funnier/tongue-in-cheek dialogue, and is 20% cooler.
The finer points:
The Achievement difference between DR2 and OTR...bit easier. For one thing, you don't have to worry about eating/clothing/using every x-type weapon anymore, you can save the BARE MINIMUM of survivors, and there are no ranked online cheeves that no one plays anymore. You DO get challenges, which are easy enough to muddle through, and without worrying too much about survivors and weapon kills to hinder your fun. Also, you can join a friend's game right before the military arrives or when 8 survivors have been collected to get the more difficult achievements and it will count for you too. In case you're lazy.
A big point to bring up is Sandbox mode. Disposing with the time limit for activities outside the main story means you have all the time in the world to waste on gambling, driving the slicecycle, tooling around with your co-op partner, beating on survivors with no guilt...the possibilities are numerous. If this were more of an independent title, with a more robust network engine, I would love to see a 16-player server, and the ability to exists in different sections. While that may be heaven, this is still nice catered island getaway.
A feature brought back (or if coming straight from DR1) is photography. I haven't seen too many people complain, and it isn't bad. Point. Click. Points. There are more than enough PP markers to get the related achievements and books will allow score increases. One thing I noticed on my profile is my photo save got corrupted (whatever that means) and asked me to delete my save data. I didn't and it plays just fine. I'm not too concerned about little pop-ups like that who have no threat.
Enough about the differences, on to the fun:
Music: Awesome head-thrashing music for the bosses, but there's nothing but zombie groans and survivor whining. I find filling with Dethmagnetic by Metallica or Pantera fills the void well.
Sound: No synch problems, already commented on dialog. Solid stuff.
Story: Plot-wise, pretty good, but this is where DR2 vanilla beats OTR. You don't go too heavy into Phenotrans and it doesn't flow into DR2: Case West. You also don't have as many emotional triggers or motivation as Chuck. Still, it's entertaining.
Main Character: Frank could easily be played by the current Bruce Campbell in the theoretical movie. Nuff said
Supporting Cast: Overactors. But in this setting, fits right in.
Video: Text has been improved yet again to be more readable, and the resolution can be turned up sharp. I found the cutscene rendering to be a little on the low-tech end, but you aren't searching for too many "Dead Rising 2 Cutscenes" on youtubers anyhow.
Tech: Load times are manageable, but still make you feel like going to another area is a hassle. A few glitched zombies here and there, but a zombie with invisible legs just adds to the funny. The engine as always, can handle an impressive about of objects instantiated on one loaded section. Kudos to that.
Controls: for K/M, they feel like they need some getting used to, but I never got used to them. I felt it was as fine-tuned as it could get when comapring to an N64 emulator, so mastery over small movement is a bust. Fortunately, this is controller-enabled, so you can switch over if you are having trouble.
Gameplay: This is the big one. I had fun. I laughed. I acted like the psychos. I fed survivors to the horde. I sent the, to their deaths to men with machine guns. And it was hilarious. Not bad for a "rereleased CAPCOM game"
Final Judgement: Buy. Play. Anticipate a sequel with Frank with fervent wonder.