I've opened an .EPS file into Affinity but it doesn't look correct, but it looks fine in Adobe Illustrator. Why?

This normally occurs when the .EPS file contains embedded Adobe Illustrator data that Affinity can't read. This is because the .EPS format doesn't support features such as blend effects, transparency, mesh fills etc.

Unfortunately, there's little we can do and we would suggest that you get a .PDF copy of the file to use in Affinity.