When asked, I eventually resorted to describing Off the Record as Super Dead Rising 2 Turbo: an updated re-release of the sort that is uniquely Capcom's style. It doesn't quite render the original game obsolete, since it's a giant ball of almost pure fan service, but it does add in a sandbox mode, and that's almost worth the $40 purchase price all by itself.
Off the Record got its start as a proposed idea for DLC: a Dead Rising 2 alternate scenario where you played as Frank West instead of Chuck Greene right from the start of the game. According to a couple of producers I talked to at E3, the project gradually gathered steam until Off the Record got big enough to justify a release as a stand-alone disc.
The end product is weird. Frank West is admittedly a big part of why the original Dead Rising became popular, but Off the Record feels like it was made for some kind of alternate universe where he became the basis of a new religion. He begins the story mode as the kind of self-obsessed jackass who routinely refers to himself in the third person, delivering his trademark lines ("I've covered wars, y'know") and dishing out one-liners with everything short of a self-aware wink at the camera.
DR2 is a distinctly wackier game than the first DR, to the point where I'd argue it actually did the game a certain amount of damage, and Off the Record is even more so. They didn't simply throw Frank into the game and call it a day; some of the more obnoxious survivors have been removed and replaced, Fortune City has abruptly acquired an amusement park with a 1950s sci-fi theme, there are two new psychopaths to fight, and the entire story mode takes a sharp left turn fairly early on. There are a lot of odd things that weren't changed at all, like many of the psychopath and survivor encounters, but most of the game is different enough to justify another run.
There's also a lot of added content, like more weapons, outfits, and combo cards, including several of the items that were unique to the Case West DLC. A lot of items and survivors in Fortune City have been moved and reshuffled, which forces you to change up your strategy fairly often; for example, you can no longer reliably pick up two defilers every time you return to the security room. They've also made a few improvements to the UI, like giving Frank a wireless earpiece so you can answer Stacey's calls on the run, and providing psychopaths with a much bigger, clearer health meter.
The big draw of Off the Record, however, is Sandbox Mode, which attaches to your save file and lets you earn levels and money to spend in the story mode, and vice versa. Sandbox Mode unlocks the entirety of Fortune City right at the start, with no timer, no need for Zombrex, and a variety of unlockable and optional challenges scattered throughout the mall. You can play through either story or Sandbox Mode in full co-op, with player two taking the role of Chuck. That alone is probably worth picking up Off the Record, as it's the game that people have wanted from this series since the first one was announced.
I'll admit, though, that Off the Record makes me a little wary of what they're planning to do with the inevitable Dead Rising 3. One of the good things about the original DR is that the entire plot is played more or less perfectly straight, and even many of the "psychopaths" are just desperate. You could completely torpedo the entire game by showing up to a tense, emotional scene in a woman's dress and a Servbot mask, sure, but that was up to you.
DR2 by comparison is some kind of colorful festival of psychotics, whether you're fighting them or rescuing them, and Off the Record is, if anything, worse. (Or, depending on your perspective, better.) One of the new psychopaths is a midget on stilts firing an ice cream gun, the aforementioned theme park is actually called "Uranus Zone," and the final fight in the story mode is one of the silliest damned things I've ever seen in a video game.
If you played through Dead Rising 2 and you're not particularly enthused about Frank, the reason to look at Off the Record is to spend a few days with a friend bouncing around the mall in Sandbox Mode. I wouldn't recommend this on any other basis, but that's pretty much enough on its own.