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I found a few notes here as to what happened with the paper in this article on the New York World. In the 20 years since the sons took over, the paper seemed to have a slow decline, part of this may be due to the editorial content, but also by the slow decline in columnists. These were a huge draw for newspapers at the time, the Journal had Nellie Bly who attracted readers, yet the most important reason may have been a price increase. The New York World was also a bright. leisurely paper as noted by Slate.com, in an era of quick news this was an expensive proposition and may have been a factor in its later years of losing money
If you look at the history of the World they had great early success with specific journalists and innovations, such as the Cross-word puzzle, but by 1920 these seemed to disappear
If you look at older editions of the New York Journal and the New York World you can definitely see this last point, in an era of newspapers coming out with morning and evening editions people would read the "broadsheets" quickly on the way to work or home. Any paper that took time to read would probably lose interest with many of the workers in New York City at the time, unless you could spend a lot of time on the paper it might lose marketshare. I also wonder, as a sociological question, if the inks used by the World were more expensive (continuing the financial losses) or came off in your hands, I'm sure the black inks from the Journal did as well and what people might have done about that.
As an aside there is also a good overview on the History of Newspapers that mentions the buyout of the World, but not much more than you already knew, but the history stretches back very far.