I think we've discussed a Tilden victory before. The consensus was that it'd be very similar to Haye's, with both being reformers and Reconstruction ending. One difference would be Paraguay would suffer more in treaty negotiations for the War of the Triple Alliance. Hayes decided Paraguay would keep the territory between the Pilcomayo River and the Verde River. With Tilden or Bristow, that might not happen.
Another effect would be the end of Republican dominance a lot earlier. There would only be 16 years of nonstop Republican rule rather than 24.