I did a few searches on OldNews.com to compare with Newspapers.com, and it seems that OldNews has a smaller database, with far fewer newspapers. It didn't contain results from a sampling of local newspapers that I tried, nor from major newspapers like the NY Times, Wall Street Journal, or Chicago Tribune.
At $99/year, OldNews is also slightly more expensive than the basic Newspapers.com subscription.
Their UX is also lacking, with poor filtering options that make it difficult to select a specific publication, city, or range of dates.
It's not clear to me how they hope to compete with the incumbent in the market.