Most of the content are there for both games, and OTR is considered a "Director's Cut" edition of the game since it has more of it, but for all intents and purposes these are two different games. Each one has a different protagonist and a slightly different story, with their own movesets/playstyles and different missions, along with items being scattered in different places that will throw you off if you played one game or the other. These games are on the short side by design, your playthru will take anywhere from 6-8 hours and no more, so there is no reason not to play both of them. I suggest playing Dead Rising 2 first and then playing OTR to appreciate all the changes the game has made. As someone who played both recently, I can't tell you which one is better even tho OTR technically has more content, each one should be judged by it's own merit.
I will you it's not all sunshine and rainbows with OTR tho, friendly AI has been dumbed down and the survivors are not nearly as strong as their DR2 counterparts. This was likely done because people joked about how little help the DR2 survivors need from you if you give them a good weapon, now even if you give them a good gun they still need to be watched carefully if you don't want them to lose huge chunks of health from zombies. OTR is also glitchier, I don't know why that is but expect to find more technical problems and weird bugs as you play OTR. There is little changes that don't make sense either in OTR, for example the Bike magazine that increases durability with the motorcycle is locked behind Case 3-2 in Dead Rising 2, giving you plenty of time to make use of it. In OTR, it is locked behind Case 7-3, in the area outside the Sergeant Psycho fight. This means that the magazine is borderline useless in the 72 hour mode with how late you get it, and it's only useful in Sandbox mode where that area is always open. DR2 has fewer issues like this, I feel it's a more stable and balanced experience even if OTR has many QoL changes and more content.