The thing to know about him is he was president for a month and then he died. That was his impact. He died. He didn't noticeably improve or worsen things (Based on his inaugural speech he might've been bad but he never got to act on it) because he had no time to because he died. Which consequently means he should be the null point we can base every other president on.
If the country was left even slightly better then you got it? Then you did a better job then Harrison. Was it left worse? Then you did worse. Did 40 presidents all make the country better and only 4 leave it worse? Tough to believe.
Just to be clear: you're talking about William Henry Harrison. We've had two presidents named Harrison; Benjamin Harrison, his grandson, was elected to the presidency half a century later and served a full term between Grover Cleveland's two terms.
It's an important distinction that a lot of people might not be aware of. Benjamin Harrison pushed legislation to ban corporate monopolies and collusion; as well as creating the concept of National Forests, which would eventually lead to the National Park service. He also tried (unfortunately unsuccessfully) to continue Lincoln's legacy by passing some major civil rights legislation, including voting rights enforcement and federal education funding for Black Americans.
Maybe I'm biased by living only a couple miles from Benjamin Harrison's house, but he was definitely a lot more consequential than his grandfather.