A lot of very bad shit, presumably. More Redeemerist assholes populating the government.
I don't think Hancock would be any worse on racial matters than Cleveland's administration was after 1884. And anyway the GOP did nothing significant for African Americans in the South after 1876.
Really, leaving aside butterfly effects, it is hard to see how the 1880 election made much difference. The tariff? The Democratic platform was ambiguous, and Hancock himself strongly denied that he would end protection for industry. (Unfortunately, he said the tariff was a "local question." He later explained privately that what he meant was that it affected different localities differently, but his statement was still ridiculed by the Republicans.
http://books.google.com/books?id=ubSem4UEn9AC&pg=PA301) Civil service reform? All the candidates said they were for it, and it would come eventually, but probably Congress would do nothing about it in the near future. (The only reason it did so in OTL was because of Garfield's assassination. So, yes, in that sense Garfield's election made a bit of a difference, but only accidentally.) The money question? Hancock was not as prominently associated with hard money as Tilden and Bayard were, but there is little likelihood he would have aligned himself with western inflationists.
Leonard Dinnerstein in “The Election of 1880,” in A. M. Schlesinger, Jr., ed., History of American Presidential Elections , 4 volumes. New York : Chelsea House and McGraw-Hill, 1971) describes the 1880 election as "one of the most insignificant in United States history." It certainly did not seem that way to voters at the time--turnout has been estimated at 78 percent. But in terms of likely actual effects on public policy, I would say Dinnerstein was right.